In this paper, we propose a novel algorithm that renders motion blurred shadows efficiently on GPUs using a temporal shadow map. Each triangle moves during a frame and for each pixel, it is visible to the light in a range of time. The main idea of our algorithm is to find such visible ranges and store in the temporal shadow map. For each sample which is visible to the camera at a certain time, we can determine whether it is shadowed or lit using visible ranges in the temporal shadow map. Thus, our algorithm solves a time-mismatch problem in the time-dependent shadow mapping algorithm. Furthermore, we use a coverage map to reduce memory footprint used for the temporal shadow map.