We propose an optimal power allocation scheme that maximizes the transmission rate of device-to-device (D2D) communications underlaying a cellular system based on orthogonal frequency division multiplexing (OFDM). The proposed algorithm first calculates the maximum allowed transmission power of a D2D transmitter to restrict the interference caused to a cellular link that share the same OFDM subchannels with the D2D link. Then, with a constraint on the maximum transmit power, an optimization of water-filling type is performed to find the optimal transmit power allocation across subchannels and within each subchannel. The performance of the proposed power allocation scheme is evaluated in terms of the average achievable rate of the D2D link.