In this paper, we investigate a secure communication system, where one transmitter sends some confidential message to one receiver, under the smart attack from one unmanned aerial vehicle (UAV). The UAV utilizes the programmable radio devices to execute multiple attack types, such as eavesdropping, jamming, and spoofing. We consider the practical communication scenarios where there are a limited number of pilot signals for channel estimation, and the channel estimation at the receiver side may be imperfect. To deal with the joint impact of smart attack and imperfect channel estimation, we use the non-cooperative game theory to propose a Q-learning-based power control algorithm in order to obtain an adaptive policy for the transmitter. In this algorithm, a Nash equilibrium strategy of the game under imperfect channel estimation is devised to maximize the utility of the transmitter and, meanwhile, suppress the smart attack from the UAV. The simulation results indicate that this strategy can effectively decrease the attack rate of the UAV attacker and increase the system secrecy capacity, regardless of the channel estimation accuracy. Moreover, the impact of the channel estimation error on the attack rate and secrecy capacity is also reflected.