FMCW LiDAR is being widely studied for its high accuracy, strong anti-interference capability and simultaneous ranging and speed measurement. The inherent fence effect of FFT will introduce errors in ranging and speed measurement. To solve this problem, firstly, this paper analyzes the law of spectrum amplitude and phase angle, and then combines with the principle of sine function, proposes a modified Rife algorithm that is easy to implement in hardware. When the estimated frequency is close to the FFT quantization frequency point, this method can effectively reduce the error of the Rife algorithm. The simulation and FPGA verification results show that when the SNR is -10 dB, the mean error (ME) and root mean square error (RMSE) of the algorithm are reduced by 69.6% and 50.7%, respectively, compared with the traditional Rife algorithm. The calculation amount is only increased by two multiplications and additions, which is negligible compared to N-point FFT computation. Finally, in order to verify the effectiveness of the algorithm, this paper build an optical test platform to simulate the intermediate frequency echo signal of LiDAR. The results show that the algorithm can achieve simultaneous ranging and speed measurement within 112 m. The ranging error is no more than 5 cm, and the speed measurement error is no more than 0.16 km/h. The algorithm meets the demand of real-time ranging and speed measurement.