Buffer-aware video streaming, which exploits the available storage space in user device to store the prefetched video data in good channels for video data use in poor channels, has been proved to have the potential to reduce the impact of fluctuating wireless channels on user-perceived video performance. However, in practical wireless networks, due to the unknown channel state and video rate, providing buffer-aware video streaming service to wireless user is a challenging problem. In this paper, with the aim to design an autonomous wireless video streaming system, we apply the deep reinforcement learning approach to dynamic resource optimization for wireless buffer-aware video streaming under unknown channel state and video rate. Specifically, we define a reward function for buffer-aware video streaming as the effective video streaming time when neither video-playback overflow nor video-playback underflow occurs. We propose a Markov decision process based problem formulation of the joint bandwidth allocation and buffer management for maximizing the effective video streaming time of all users. The optimal bandwidth allocation and buffer management policy is learned from training a deep neural network based on a deep reinforcement learning algorithm. We simulate the proposed algorithm in Tensorflow. Simulation results verify that the proposed deep reinforcement learning approach is effective for buffer-aware video streaming in wireless networks.