Non-orthogonal multiple access (NOMA) is a promising scheme for flexible passive optical networks (PONs), which provides high throughput and overall improved system performance. NOMA with the successive interference cancellation (SIC)-based receiver, which is used to detect the multiplexed signal in a sequential fashion, requires perfect channel state information and suffers from the error propagation problem. In this paper, we propose a convolutional neural network (CNN) based signal demodulation method for NOMA-PON, which performs channel estimation and signal detection in a joint manner. The CNN is first trained offline using the captured data for a given received optical power and then used to recover the data stream directly in the online mode. We show by experimental demonstration that, the proposed CNN-based receiver (Rx) outperforms the conventional SIC-based Rx and is more robust to the nonlinear distortion. We show that for the CNN-based system with 20 km optical fiber, the required received optical power levels at a bit error rate (BER) of 1×10−3 are lower by 4, 3 and 2.5 dB for power allocation ratios of 0.16, 0.25, 0.36, respectively compared with SIC-based system. In addition, the BER performance of CNN deteriorates considerably less with non-linear distortion compared with SIC.