Laser chaotic communication system is widely used in the field of secure communication due to its unique advantages such as strong randomness, quasi-noise, and high bandwidth of chaotic signals. At present, laser chaotic synchronization communication generally depends on the laser internal nonlinear effect or photoelectric oscillator. Still, it is difficult to achieve high-quality synchronization communication because of the difficulty of hardware parameters matching between the transmitter and the receiver. Aiming at this shortcoming, some scholars have proposed to use the powerful nonlinear fitting ability of a neural network to model the receiver of a chaotic optical communication system, to realize high-quality synchronization communication. This paper proposes to use the long short-term memory neural network for the mathematical modeling of the chaotic optical transmitter. It successfully solves the problems of complex hardware systems and low synchronization coefficients in traditional chaotic optical communication and provides a reference for point-to-multipoint chaotic communication.This paper presents the design of a laser chaotic synchronization communication system based on long short-term memory neural network, and uses a cross-prediction algorithm to optimize the network model. In the off-line training stage, a large number of chaotic encrypted signals generated by the transmitter are used as input variables of the neural network, and the real chaotic carrier sequence is further selected by the cross-prediction algorithm as output variables of the neural network. To enable the long short-term memory neural network to accurately predict the output variables according to the input variables, each training iteration of the network will update its node state until the ideal loss value is reached. In the test stage, the node state of the neural network has been determined. When the input variable is received, the system will automatically map the predicted carrier sequence, and the received encrypted signal can be directly subtracted from the predicted carrier sequence to decrypt useful information. The scheme achieves a high synchronization coefficient and achieves high-quality chaotic synchronization communication.The simulation result consists of three parts. The first is the quality of decrypted information at the receiver end. After modeling and training of laser chaotic system by long short-term memory neural network, the system has good prediction effect and high-quality chaotic synchronization. The synchronization coefficient between the real target carrier and the predicted carrier is more than 99.9%, and the root means the square error is as low as 10^-3. The noisy information is demodulated directly from the encrypted information minus the chaotic carrier predicted by the neural network, and the bit error rate is as low as 10^-10. It is far lower than the hard decision threshold of the forward error correlation standard, which is 3.8$\times$10^-3. To verify the universality of the system, the simulation of optical feedback and photoelectric feedback synchronization communication system has the same level of communication quality. Secondly, the influence of the number of network nodes, the information coupling coefficient, and the signal-to-noise ratio on the chaotic synchronization communication performance is studied in the optical feedback chaotic synchronization communication system. The results show that when the coupling coefficient is 0.08, the signal-to-noise ratio is 30 dB unchanged, and the number of nodes is between 200 and 800, the system has good bit error rate performance, and the maximum is only 10^-10. When the number of nodes is 300, the synchronization coefficient reaches the peak value of 0.999 93. When the number of nodes reaches 1 000~1 200, the neural network appears overfitting state, and the information appears with certain distortion. This paper further studies the effect of nodes in the range of 40~240 on system performance. In the case of a few nodes, the synchronization coefficients of the system are all above 0.999 8, the bit error rate is far lower than the hard decision threshold of forward error correlations standard, and the bit error rate is lower than 10^-8 magnitude. When the number of network nodes is 240, the maximum synchronization coefficient is 0.999 96. For the coupling coefficient, the number of nodes is kept at 200 and the signal-to-noise ratio is unchanged at 30 dB. When the coupling coefficient is large and reaches 0.04~0.12, the bit error rate of the system can reach a relatively low level stably, all of which are lower than 10^-6, and the system communication quality is good. At the same time, when the coupling coefficient reaches 0.11, the maximum synchronization coefficient of the system is 0.999 95. For the signal-to-noise ratio, keep the network nodes 200, the coupling coefficient 0.08 unchanged, the signal-to-noise ratio between 5~40 dB, and the system synchronization coefficient can reach above 0.999 8. When the signal-to-noise ratio reaches 15 dB, the bit error rate reaches the order of 10^-6, far lower than the hard decision threshold of the forward error correlations standard. When the signal-to-noise ratio is 25 dB, the synchronization coefficient reaches the peak value, which is 0.999 966. Finally, to verify the actual availability of the system, the grayscale image of 256$\times$256 is successfully transmitted in the optical feedback system. In addition, the system security is analyzed from three aspects: brute force search, plaintext attack, and ciphertext attack. The results show that the system can resist many attacks and has high security.The proposed laser chaotic synchronization communication based on long short-term memory neural network and the network structure optimization by cross-prediction algorithm achieves high-quality chaotic synchronization communication in both optical feedback and photoelectric oscillator system. This scheme successfully solves the problems of complex hardware systems and low synchronization coefficients in traditional chaotic optical communication. Then, the influence of long short-term memory neural network nodes, coupling coefficient, and signal-to-noise ratio on the communication performance of the system is studied. When there are more nodes or the coupling coefficient is low, the decryption information will appear with a certain distortion. Finally, the feasibility of this scheme is further verified by image transmission. As a whole, the synchronization coefficient of the system can be as high as 0.999 966, and the bit error rate is as low as 10^-10, which realizes high-quality chaotic synchronization communication. The advantages of this scheme are as follows. First, long short-term memory neural network, with its long-term dependence on learning time series and strong robustness, enables this scheme to achieve high-quality synchronous communication in both optical feedback and photoelectric feedback systems and has certain universality. Second, in the chaotic synchronous communication system based on long short-term memory neural network in this paper, the system performance obtained by the state of a few nodes and multiple nodes is outstanding. Choosing the state of a few nodes can greatly reduce the time loss and save the time cost of training neural networks. Third, the long short-term memory neural network scheme proposed in this paper successfully solves the problem of hardware parameter matching between the two receivers in traditional chaotic optical communication and has the advantages of convenience and security, which provides a thought for the subsequent research of chaotic optical communication.