The fundamental structure of all-optical dual-hop free-space optical communication (FSO) system is presented and the composite fading channel model which includes atmospheric loss, atmospheric turbulence and pointing errors is established. In the full channel state information relaying, subcarrier intensity modulation is adopted. The closed-form expressions for outage probability and bit-error rate (BER) of dual-hop FSO systems are derived, based on the effects of background noise and amplified spontaneous emission noise. Then the outage probability of dual-hop FSO system is compared with that of the direct link. The effects of the parameters, such as signal-to-noise ratio, the average transmitted photon count of the source node (SN) and optical degree-of-freedom, on the outage probability and bit-error rate are also researched. The results show that all-optical dual-hop relaying can significantly improve the performance of the systems.