To take advantages of the high spectral efficiency of full-duplex (FD) mode and control rate reduction caused by the self-interference introduced to the relay receiver, a novel hybrid duplex scheme is proposed where the relay works in FD mode following a duty cycle, and receives-only for the rest of time. After characterizing the achievable rate, a joint FD duty cycle and source power allocation problem is formulated to maximize the achievable rate. It is proved that the optimal source power allocation follows a water-filling algorithm over time. Moreover, the optimal FD duty cycle is obtained by considering low-, medium-, and high-source power cases. Specially, closed-form approximation of the optimal FD duty cycle for medium-source power case is presented. Besides, it is shown that the proposed hybrid duplex scheme degenerates to half-duplex and FD modes for low-and high-source power cases, respectively. Numerical results demonstrate that the proposed scheme can effectively improve the achievable rate for a wide range of parameters.