In order to detect weak light from background radiation, utilizing an array of Geiger-mode avalanche photodiodes (GM-APDs) as a detector in the receiver is researched. First, the principle of a GM-APD operated in gated mode is analyzed. Based on the Poisson random process of arrival of photons, the trigger probability of a single GM-APD has been computed. Then, according to the trigger probability, a new bit error rate (BER) model of a photon-counting array receiver system is built, and the expression of BER is derived based on the quantum efficiency, signal photons, background photons, dark carriers, and the number of GM-APDs in array. Using the BER expression, the error performance of a new photon-counting array receiver system can be predicted rapidly. Furthermore, the error performance of a system based on an array of GM-APDs is investigated. The simulation results indicated that maintaining the ratio of signal photons and background photons above 1 is necessary for system operation. When background noise is limited to the acceptable range, maintaining a certain scale of GM-APDs (above 20) in array can greatly reduce the demand of transmitting power. Compared with achieving target BERs of 10-6 and 10-9, preserving a BER of 10-3 and making use of error correction coding can further improve the receiving sensitivity to 5-8 dB.