For atmospheric weak turbulence channel model with lognormal distribution,polar code is adopted to improve the FSO system transmission performance.A new BP decoder based on a modified 3×3 kernel matrix is proposed.The kernel matrix,code-rate and the calculation formula for the basic unit were redefined.BER performance of the polar codes with the new BP decoder and the traditional BP decoder was compared and analyzed.The numerical results show that the proposed method has a lower bit error rate compared with the traditional BP decoder.More importantly,the message memory requirement can be reduced and the time delay can be reduced.Under the longer code-word length,the performance of FSO system is much improved.