Relay using analog network coding (ANC) can achieve the same maximum throughput as the direct transmission while reducing the required transmit power. In this paper, we propose an adaptive power allocation scheme for bidirectional single-carrier (SC) ANC. The proposed scheme adaptively allocates the transmit power so as to make the instantaneous signal-to-interference plus noise power ratios (SINRs) of both up and down links identical and maximized. Since it is quite difficult to obtain the optimal solution, we derive an approximate solution. We evaluate, by computer simulation, the distributions of bit error rate (BER) and throughput when using the proposed power allocation. It is shown that the proposed scheme can improve the BER and throughput performances compared to equal power allocation.