Adaptive interleaving method implemented by a hybrid system is proposed to deal with burst errors caused by long and deep channel fades in free space optical communications (FSOC) through atmospheric turbulence. Actually, considerable memory can be saved by changing the interleaving depth at transmitter and receiver according to the updated burst information from channel estimator. Combining with error correcting codes, anti-burst performance of the proposed method is evaluated by simulations based on channel state information from laser transmission experiments over an 11.8 km urban link. Simulation results show that 1~2 or even higher orders of magnitude of a memory can be saved when comparing with the maximum memory interleaving. The results have proved that the cost of anti-burst performance can be minimized to 10% or even smaller by the adaptive interleaving method when joint use with error correcting codes.