Recently, the emerging bio-inspired event cameras have demonstrated potentials for a wide range of robotic applications in dynamic environments. In this paper, we propose a novel fast and asynchronous event-based corner detection method which is called FA-Harris. FA-Harris consists of several components, including an event filter, a Global Surface of Active Events (G-SAE) maintaining unit, a corner candidate selecting unit, and a corner candidate refining unit. The proposed G-SAE maintenance algorithm and corner candidate selection algorithm greatly enhance the real-time performance for corner detection, while the corner candidate refinement algorithm maintains the accuracy of performance by using an improved event-based Harris detector. Additionally, FA-Harris does not require artificially synthesized event-frames and can operate on asynchronous events directly. We implement the proposed method in C++ and evaluate it on public Event Camera Datasets. The results show that our method achieves approximately 8× speed-up when compared with previously reported event-based Harris detector, and with no compromise on the accuracy of performance.