When optical chaos communication system is applied to space optical communication, some necessary structural modifications are needed, and atmospheric effects are required to be considered. As one of these effects, beam spreading can affect the bit error rate (BER) of space optical chaos communication system under nonzero detector mismatch. To study the specific effect of beam spreading on the system BER, we make a formula modification including this effect. And based on the derived formula, we conduct a numerical simulation of the system BER under different detector mismatches. In our numerical simulation, we select the five typical system parameters of such system, which are synchronization error, zenith angle, transmitting power, divergence angle, and receiving diameter, and obtain their relationships with the BER. Corresponding discussions are made according to our results, which are beneficial to practical application of space optical chaos communication system.