Designing the optimum receiver for different channel conditions is a difficult task, because the required channel statistics are usually not known at the receiver. In this study, we propose a neural network (NN) based approach to demodulate the transmitted signal over fading channels. The novelty of the resulting scheme lies in the combination of channel estimation, equalization, and demodulation procedures in a single NN structure. We assess the performance of the proposed receiver for Rayleigh fading channels. It is demonstrated that the Rayleigh theoretical bound may be achieved by the proposed receiver if the frame structure has a sufficient pilot duration in the training mode. It is also shown that the proposed receiver is robust for low SNR cases.