In this paper, the optimal power schedule is studied for the wireless communication network under Denial-of-Service (DoS) attacks. Different from Nash Equilibrium (NE), a Stackelberg Equilibrium (SE) framework is proposed to analyze the game between the defender and the attacker under two different types of incomplete information. In the first scenario, the defender only knows the statistical characteristics about whether the attacker exists or not, which means that the defender knows the probability that there is only background noise on the environment. In the second situation, the defender does not know the total power of the attacker exactly and only acquires to know the total power with certain probability. Moreover, the detailed steps of designing both players' optimal strategies are given and analyzed. Adaptive Penalty Function (APF) approach and Differential Evolution (DE) algorithm are combined to deal with the corresponding nonlinear and non-convex optimization issues. Finally, examples are provided to illustrate the results proposed in this work. (C) 2018 Elsevier Ltd. All rights reserved.