Multiple Object Tracking is an important task for autonomous vehicles. However, it gets difficult to track objects when it is hard to detect them due to occlusion or distance to the sensors. We propose a method, "GridTrack", to overcome this difficulty. We fuse a dynamic occupancy grid map (DOGMa) with an object detector. DOGMa is obtained by applying a Bayesian filter on raw sensor data. This improves the tracking of the partially observed / unobserved objects with the help of the Bayesian filter on raw data, which has a powerful prediction capability. We develop a network to track the objects on the grid and fuse information from previous detections in this network. The experiments show that the multi-object tracking accuracy is high with the usage of the proposed method.