An orbital angular momentum division multiplexing free space optical communication (OAM-DM FSO) system with channel coding can compensate atmospheric channel fading and improve system performance. An OAM-DM FSO system based on hybrid channel coding is proposed in this paper. The coding gain is improved by taking into account mode dependent channel fading difference caused by atmospheric turbulence. Simulation results show that compared with single channel coding, the coding gain is increased by 1.85 dB under Cn2=1E-14, BER=1E-5 with non-uniform LDPC code (0.7 code rate) for an OAM1/OAM3 multiplexing system. In addition, for four OAM modes (+1,+3,+5,+7) multiplexing systems, the coding gain is increased by more than 3.8 dB under Cn2=1E-14 and BER=1E-5.