In wireless communication, signal demodulation under non-ideal conditions is one of the important research topic. In this paper, a novel non-coherent binary phase shift keying demodulator based on deep neural network, namely DeepDeMod, is proposed. The proposed scheme makes use of neural network to decode the symbols from the received sampled signal. The proposed scheme is developed to demodulate signal under fading channel with additive white Gaussian noise along with hardware imperfections, such as phase and frequency offset. The time varying nature of hardware imperfections and channel poses a additional challenge in signal demodulation. In order to address this issue, additionally we propose transfer learning based DeepDeMod scheme. Pilot symbols along with data is transmitted in a packet which is used to learn the time varying parameters from the pilot reception followed by data demodulation. Results show that compared with the conventional demodulators and other machine learning based demodulators, our proposed DeepDeMod provides significantly better performance in term of bit error rate. We also implement the proposed DeepDeMod on software defined radio and present the experimental results.INDEX TERMS Binary phase shift keying (BPSK), deep neural network (DNN), demodulation, softwaredefined radio (SDR), transfer learning, universal software radio peripheral (USRP).