Free-space laser communication has a wide range of application prospects in the field of wireless communication due to its high transmission rate, good security performance, small volume and mass. It can effectively solve the problems of low communication rate and large volume in microwave communication, especially in the satellite field. In order to realize a long-distance, high-speed inter-satellite laser communication system, it is necessary to introduce a digital laser communication receiver to flexibly suppress interference and noise and improve communication sensitivity. According to the principle of digital communication error probability, a digital receiver based on field programmable gate array (FPGA) is designed. Filtering algorithms such as finite impulse response, dynamic threshold and baseband median are used to optimize the signal-to-noise ratio and improve detection sensitivity. At the same time, the sensitivity testing experimental structure of the 1 550 nm laser communication receiver is designed, and the sensitivity testing experiment is carried out. Experimental results show that the avalanche photo diode (APD) receiver achieves a detection sensitivity of -52.57 dBm close to the theoretical design value at a communication rate of the order of Mbps. The signal-to-noise ratio is increased by about 10 dB through the digital filtering algorithm, which provides theoretical guidance for the receiver design of satellite laser communication.