Autonomous navigation in unknown complex environment is still a hard problem, especially for small Unmanned Aerial Vehicles (UAVs) with limited computation resources. In this paper, a neural network-based reactive controller is proposed for a quadrotor to fly autonomously in unknown outdoor environment. The navigation controller makes use of only current sensor data to generate the control signal without any optimization or configuration space searching, which reduces both memory and computation requirement. The navigation problem is modelled as a Markov Decision Process (MDP) and solved using deep reinforcement learning (DRL) method. Specifically, to get better understanding of the trained network, some model explanation methods are proposed. Based on the feature attribution, each decision making result during flight is explained using both visual and texture explanation. Moreover, some global analysis are also provided for experts to evaluate and improve the trained neural network. The simulation results illustrated the proposed method can make useful and reasonable explanation for the trained model, which is beneficial for both non-expert users and controller designer. Finally, the real world tests shown the proposed controller can navigate the quadrotor to goal position successfully and the reactive controller performs much faster than some conventional approach under the same computation resource.