This paper proposes an optimal power allocation method for two-way decode-and-forward relay networks with equal transmit power at source nodes when channel coefficients are the same. It analytically determines the optimal power values for the two source nodes and one relay node, which maximize the achievable sum rate under a sum power constraint for given channel coefficients. Numerical results show that the proposed optimum power allocation scheme achieves a higher achievable sum rate than the equal power allocation scheme.