In order to achieve optical wireless communication in condition of strong attenuation, the signal photons which arrive at receiver are detected by single photon avalanche detector. The principle of Geiger-mode avalanche photodiode detector (Gm-APD) operating in gated mode is analyzed. Based on the Poisson distribution, the trigger probability of Gm-APD in a gate is researched. According to the binomial distribution, the bit error rate (BER) model of single Gm-APD is built. It is researched that how BER varies with signal photons per gate, background photons per gate and the number of gates per bit. Theory and simulation results show that the best BER performance is determined by the number of gates per bit; the BER decreases exponentially with the increase of gates per bit, and the receiving sensitivity can be improved at least 3 dB under BER of 10^-3 compared to BER of 10^-9. Finally, the BER obtained by experiment under the given conditions is compared with simulation results, which shows the validity of the BER model.