Free space optics (FSO) is attractive for the 'last mile' communication in recent years for many combining advantages of fiber communication and other wireless technologies. FSO can provide high data rate with low power consumption, high immunity to interference, convenient deployment and flexibility. Optical system is an important section in the FSO transceiver terminal. In this paper the design of optical system based on a single Galileo telescope for both transmit and receive is proposed, and a polarization beam splitter is adopted to apart the receiving light from transmitting light. The configuration can avoid interference from the retroreflecting light of the ocular effectively. Some factors that affect the performance of the optical system are analyzed, such as the geometrical spreading loss and the loss increment according to pointing error and telescope maladjustment. Power budget shows that the system can satisfy the need of access for 1km in the light fog, and 2km in the thin fog.