According to the complexity of photon motion under water caused by absorption and scattering attenuation, this paper establishes a photon spatio-temporal random channel model based on the tracked underwater single-photon motion state. Considering different types of water qualities, link distances, receiving apertures, launching angles, and field of view angles, the relevant information of the photons arrived at the receiving end was counted and the factors influencing optical receiving intensity and channel impulse response based on underwater single-photon communication system were studied. At the same time, comprehensively considering the photon emission, underwater photon movement process, detector characteristics, and synchronization signal extraction method, etc., a data demodulation scheme based on photon counting in the time slot was adopted and the system performance was analyzed. The simulation results show that the launching angle and receiving aperture are the main factors that affect the delay broadening. The larger the receiving aperture, the smaller the system bit error rate (BER); the larger the link distance, launching angle, and noise factor, the larger the system BER. The theoretical communication distance is about 185 m. The results well describe the characteristics of underwater photon scattering and pulse delay broadening.