Abstract: The performance of multi-hop coherent orthogonal frequency division multiplexing (OFDM) free space optical (FSO) system is studied by using quadrature phase shift keying (QPSK) modulation in this paper. A generalized model called M distribution is selected, which is suitable for all categories of turbulence ranging from weak to strong and characterizes other existing statistical models of atmospheric turbulence induced fading as its special case. The system uses decode and forward (DF) relay protocol between the transmitter and receiver of the relay auxiliary link. Considering the joint attenuation effects of atmospheric turbulence, path loss and pointing error on the atmospheric channel fading model, we derive the Meijer G closed-form expressions of outage probability and symbol error rate (SER). Furthermore, the effects of key factors, such as relay link length, the number of relay nodes and subcarriers on the outage and SER performance of OFDM FSO system are analyzed through simulations. This work lays a theoretical foundation for the practical application of the relay system.