The free-space optical communication based on 8-ary orbital angular momentum shift keying (8OAM-SK), where information can be encoded as the OAM state of light, is studied. We implement a numerical simulation using a phase screen model for atmospheric turbulence, which is based on the Fourier transformation method, to analyze the influence of atmospheric turbulence. The bit error rate performance of the 8OAM-SK system is investigated in several different conditions. The numerical simulations demonstrate that higher received power is required in stronger turbulence to achieve acceptable signal quality. It is also revealed that lower data rate shows better tolerance to the turbulence strength.