This paper proposes a long reach passive optical network based on power-domain non-orthogonal multiple access for the next generation optical access network. Based on channel estimation function, the traditional power-domain non-orthogonal multiple access networks employ successive interference cancellation (SIC) algorithm for signal demodulation and recovery, which require accurate channel estimation and has error propagation problem. To overcome this problem, a signal receiving scheme based on modified convolutional neural network (CNN) is proposed, which exploits a large amount of data to independently fit the channel function of each user, thus to break the dependence chain between users in the SIC demodulation algorithm, and improve transmission performance and fairness of the system. The results show that, compared with the traditional SIC demodulation algorithm in the long reach power-domain non-orthogonal multiple access passive optical network, the receiving scheme based on the modified CNN can improve the transmission performance of far-end users (transmission 60 km) and near-end users (transmission 20 km) by about 0.5 dB and 1.7 dB, respectively, and its fairness index closer to 1.