In this paper, a turbo-coded FSO system with Mary pulse position modulation is considered over log-normal turbulence channels and an adaptive coding and modulation scheme is proposed under peak power constraints. In the proposed system, a link adaptation technique is designed to maximize the bandwidth efficiency of the turbo-coded FSO system by adaptively varying the code rate of turbo code and modulation size according to the channel state information. The simulation results demonstrate significant performance improvements of the proposed adaptive coding and modulation scheme over coded/uncoded adaptive modulation and non-adaptive counterparts.