In this paper, a power allocation algorithm of dual-function radar–communication system with limited power is proposed to obtain better overall system performance measured by the weighted summation of radar signal to interference plus noise ratio (SINR) and communication channel capacity. First, a power allocation model is established to maximize the radar SINR and communication channel capacity with limited transmitted power. Then, the Karush–Kuhn–Tucker (KKT) conditions are used to solve the optimal objective function under the condition that only radar SINR or communication channel capacity is considered, respectively. Finally, the optimal value is combined with the original model and transformed into a single objective optimization model, and the optimal power is obtained by solving the model through the iterative optimization algorithm. Simulation results show that, compared with other power allocation algorithms, the proposed algorithm can achieve better radar-communication integration performance under the same transmit power.