With the advanced development of image processing technology, visible light positioning (VLP) system based on image sensors has attracted more and more attention. However, as a commonly used light receiver, traditional CMOS camera has limited dynamic range and high latency, which is susceptible to various lighting and environmental factors. Moreover, high computational cost from image processing is unavoidable for most of visible light positioning systems. In our work, a novel VLP system using an event-based neuromorphic vision sensor (event camera) as the light receiver is proposed. Due to the low latency and microsecond-level temporal resolution of the event camera, our VLP system is able to identify multiple high-frequency flickering LEDs in asynchronous events simultaneously leaving out the need for data association and traditional image processing methods. A multi-LED fusion method is applied and a high positioning accuracy of 3cm is achieved when the height between LEDs and the event camera is within 1m.