To reduce the amount of transmitted data, feature map-based fusion is recently proposed as a practical solution to cooperative 3-D object detection by autonomous vehicles (AVs). The precision of object detection, however, may require significant improvement, especially for objects that are far away or occluded. To address this critical issue for the safety of AVs and human beings, we propose a cooperative spatial feature fusion (CoFF) method for AVs to effectively fuse feature maps for achieving a higher 3-D object detection performance. Especially, CoFF differentiates weights among feature maps for a more guided fusion, based on how much new semantic information is provided by the received feature maps. It also enhances the inconspicuous features corresponding to far/occluded objects to improve their detection precision. The experimental results show that CoFF achieves a significant improvement in terms of both detection precision and effective detection range for AVs, compared to previous feature fusion solutions.