Laser speckle imaging (LSI) is a powerful tool for motion analysis owing to the high sensitivity of laser speckles. Traditional LSI techniques rely on identifying changes from the sequential intensity speckle patterns, where each pixel performs synchronous measurements. However, a lot of redundant data of the static speckles without motion information in the scene will also be recorded, resulting in considerable resources consumption for data processing and storage. Moreover, the motion cues are inevitably lost during the "blind" time interval between successive frames. To tackle such challenges, we propose neuromorphic laser speckle imaging (NLSI) as an efficient alternative approach for motion analysis. Our method preserves the motion information while excluding the redundant data by exploring the use of the neuromorphic event sensor, which acquires only the relevant information of the moving parts and responds asynchronously with a much higher sampling rate. This neuromorphic data acquisition mechanism captures fast-moving objects on the order of microseconds. In the proposed NLSI method, the moving object is illuminated using a coherent light source, and the reflected high frequency laser speckle patterns are captured with a bare neuromorphic event sensor. We present the data processing strategy to analyze motion from event-based laser speckles, and the experimental results demonstrate the feasibility of our method at different motion speeds.