Non-orthogonal multiple access (NOMA) is a promising scheme to improve the spectral efficiency, user fairness, and overall throughput in visible light communication (VLC) systems. However, the error propagation (EP) problem together with linear and nonlinear distortions induced by multipath, limited modulation bandwidth and nonlinearity of light emitting diode significantly limit the transmission performance of NOMA-VLC systems. In addition, having accurate channel state information, which is important in the recovery of NOMA signal, in mobile wireless VLC systems is challenging. In this work, we propose a convolutional neural network (CNN) based demodulator for NOMA-VLC, in which signal compensation and recovery are jointly realized. Both simulation and experiment results show that, the proposed CNN based demodulator can effectively compensate for both the linear and nonlinear distortions, thus achieving improved bit error ratio (BER) performances compared with the successive interference cancellation (SIC) and joint detection based receivers. Compared to SIC, the performance gains are 1.9, 2.7 and 2.7 dB for User1 for power allocation ratios (PARs) of 0.16, 0.25 and 0.36, respectively, which are 4, 4 and 2.6 dB for User2 for PARs of 0.16, 0.25 and 0.36, respectively.