With the help of special neuromorphic hardware, spiking neural networks (SNNs) are expected to realize artificial intelligence with less energy consumption. It provides a promising energy-efficient way for realistic control tasks by combing SNNs and deep reinforcement learning (RL). There are only a few existing SNN-based RL methods at present. Most of them either lack generalization ability or employ Artificial Neural Networks (ANNs) to estimate value function in training. The former needs to tune numerous hyper-parameters for each scenario, and the latter limits the application of different types of RL algorithm and ignores the large energy consumption in training. To develop a robust spike-based RL method, we draw inspiration from non-spiking interneurons found in insects and propose the deep spiking Q-network (DSQN), using the membrane voltage of non-spiking neurons as the representation of Q-value, which can directly learn robust policies from high-dimensional sensory inputs using end-to-end RL. Experiments conducted on 17 Atari games demonstrate the effectiveness of DSQN by outperforming the ANN-based deep Q-network (DQN) in most games. Moreover, the experimental results show superior learning stability and robustness to adversarial attacks of DSQN.