This paper considers a hybrid relay network consisting of the source, the amplify-and-forward (AF) relay, the decode-and-forward (DF) relay, and the destination. We propose the optimal power allocation schemes between two different relays which maximize the achievable rate under a sum relay power constraint for given channel gains and transmit power from source. By solving the optimization problem to maximize the achievable rate for each relay network, the transmit power values in closed-form are derived. When the channel gains are the same, the optimal power allocation scheme for AF-DF relay network proves that a more power should be allocated at the first relay to maximize the achievable rate. In case of the DF-AF relay network, we derive the optimal power allocation scheme for the possible four cases. Under the same SNR condition at the first hop, we show that the achievable rate of AF-DF relay network is greater than that of DF-AF relay network when the channel gain between two relays is higher than that between the second relay and destination. Simulation results show that the proposed power allocation schemes provide a higher achievable rate than the equal power allocation schemes.