Combining half-duplex (HD) and full-duplex (FD) is promising in improving the information transmission rate of relay channels. This work proposes a novel two-phase hybrid duplex scheme for Gaussian relay channel where the relay operates in FD mode for a fraction of time and only transmits information for the rest of time. The achievable rate of the proposed hybrid duplex scheme is characterized in detail. Based on the obtained result, a joint time division and power allocation problem is formulated to maximize the achievable rate. In particular, the formulated problem is solved through a two-step optimization method. Firstly, the optimal relay power allocation is obtained for given time division factors. Then, the achievable rate maximization problem is addressed by finding the optimal time division factors. The closed-form expression for the maximal achievable rate is derived for some specific cases. Numerical results show that the proposed two-phase hybrid duplex scheme significantly improves the achievable rate of Gaussian relay channel compared with existing benchmark schemes.