Organic scintillation detectors like BC501A, BC519, NE213, etc. have an inherent ability to classify neutrons and γ-rays through a process known as pulse shape discrimination (PSD). We developed a deep neural network (DNN)-based machine learning algorithm to discriminate neutrons/γ-rays. The algorithm was trained with data obtained from a BC501A detector considering the Cf-252 source. Further, to assess the performance of the DNN-based PSD algorithm, the algorithm was tested with an independent data set acquired with a different source-detector set-up, namely, BC501 detector with Am–Be source and a different digitiser. Results indicate that our proposed algorithm can successfully discriminate the neutrons and γ-rays with reasonably good accuracy for the independent data set.