Aiming at the shortcomings of the heavy computational complexity in existing random access preamble algorithm, a 5G random access preamble detection algorithm is proposed. First, the received signal is processed by the inverse process of the transmitting end to obtain a frequency domain preamble. Then a frequency domain ZC sequence is generated and grouped, and the ZC sequences in each group are correlated with the frequency domain preamble. Finally, the threshold is detected by setting a threshold. The sequence uses a multi-antenna diversity combing to modify the Cumulative Distribution Function（CDF） of the relative threshold, and determines an absolute detection threshold. The threshold is a product of the relative detection threshold and the time-varying noise level, based on the relative detection threshold. The simulation results show that compared with the frequency domain fixed threshold preamble detection algorithm, the correct detection probability performance of the proposed algorithm is improved by 1 dB in the Additive White Gaussian Noise (AWGN) channel. In the Tapped Delay Line (TDLC300-100) channel, the correct detection probability performance of the proposed algorithm is improved by 2 dB.