With the rapid development of underwater sensor networks, the design of underwater demodulators become increasingly significant. However, underwater acoustic communication is faced with many problems such as propagation time delay, multipath effect and Doppler effect due to the complexity of underwater environment. Demodulation of underwater communication signals is a challenging task. To solve this problem, we propose a novel binary phase shift keying (BPSK) demodulator for underwater acoustic communication based on convolutional neural network, which demodulates the modulation data by detecting the position of phase shift. The method proposed in this paper significantly reduces the bit error rate (BER) compared with the results of the traditional method in URPC1 datasets (Underwater Robot Picking Contest).