Event cameras, or dynamic vision sensors, have recently achieved success from fundamental vision tasks to high-level vision researches. Due to its ability to asynchronously capture light intensity changes, event camera has an inherent advantage to capture moving objects in challenging scenarios including objects under low light, high dynamic range, or fast moving objects. Thus event camera are natural for visual object tracking. However, the current event-based trackers derived from RGB trackers simply modify the input images to event frames and still follow conventional tracking pipeline that mainly focus on object texture for target distinction. As a result, the trackers may not be robust dealing with challenging scenarios such as moving cameras and cluttered foreground. In this paper, we propose a distractor-aware event-based tracker that introduces transformer modules into Siamese network architecture (named DANet). Specifically, our model is mainly composed of a motion-aware network and a target-aware network, which simultaneously exploits both motion cues and object contours from event data, so as to discover motion objects and identify the target object by removing dynamic distractors. Our DANet can be trained in an end-to-end manner without any post-processing and can run at over 80 FPS on a single V100. We conduct comprehensive experiments on two large event tracking datasets to validate the proposed model. We demonstrate that our tracker has superior performance against the state-of-the-art trackers in terms of both accuracy and efficiency.