Event cameras have many advantages over conventional frame-based cameras, such as high temporal resolution, low latency and high dynamic range. However, state-of-the-art event- based algorithms either require too much computation time or have poor accuracy performance. In this paper, we propose an asynchronous real-time corner extraction and tracking algorithm for an event camera. Our primary motivation focuses on enhancing the accuracy of corner detection and tracking while ensuring computational efficiency. Firstly, according to the polarities of the events, a simple yet effective filter is applied to construct two restrictive Surface of Active Events (SAEs), named as RSAE+ and RSAE−, which can accurately represent high contrast patterns; meanwhile it filters noises and redundant events. Afterwards, a new coarse-to-fine corner extractor is proposed to extract corner events efficiently and accurately. Finally, a space, time and velocity direction constrained data association method is presented to realize corner event tracking, and we associate a new arriving corner event with the latest active corner that satisfies the velocity direction constraint in its neighborhood. The experiments are run on a standard event camera dataset, and the experimental results indicate that our method achieves excellent corner detection and tracking performance. Moreover, the proposed method can process more than 4.5 million events per second, showing promising potential in real-time computer vision applications.