In recent years, there have occurred many incidents that unmanned aerial vehicles (UAVs) in the field of national security. While in some situations, UAVs may be deployed simultaneously by different parties with opposite purposes, easily resulting in direct competitions against each other. In this case, how to use UAVs to pursue UAVs has become a hot spot. In order to analyze the behavior of UAV, building a realistic mathematical dynamic model is necessary. In this paper, we propose a Takagi-Sugeno (T-S) fuzzy control system based UAV dynamic model, which is exactly the same UAV control method in practice. To address the competition conundrum between UAVs, we formulate this problem into a pursuer-evader problem and leverage the reinforcement learning based machine learning method to solve this. The proposed deep Q network is based on traditional Q learning but able to address some deficiencies. Basically, deep Q network has three vital improvements: using neural network to describe the Q function, the architecture of double networks, and the experience replay. The simulation results show the correctness of our analysis and effectiveness of our proposed method.