In order to further improve the speed and reliability of atmospheric optical communication systems, a back-propagation(BP) neural network assisted signal detection method is proposed to improve the bit error rate for pulse position modulation(PPM) and quadrature phase shift keying(QPSK) hybrid modulated faster-than-Nyquist(FTN) atmospheric optical communications system. BP neural network is utilized to extract the channel characteristics, which improves the bit error performance of the system in time-varying atmospheric channels. The simulation results show that compared with the maximum likelihood detection, the system bit error performance can be improved by 2.0 dB and 1.5 dB when the acceleration factor is 0.8, the bit error ratio is 10-3, and the roll off factor is 0.6 and 0.7, respectively. When the acceleration factor is 0.8, the bit error ratio is 10-4, and the roll off factor is 0.8 and 1, the system bit error performance can be improved by 2.0 dB and 1.8 dB, respectively.