In this paper, we propose a novel form of the loss function to increase the performance of LiDAR-based 3D object detection and obtain more explainable and convincing uncertainty for the prediction. The loss function was designed using corner transformation and uncertainty modeling. With the new loss function, the performance of our method on the vat split of KITTI dataset shows up to a 15% increase in terms of Average Precision (AP) comparing with the baseline using simple Ll Loss. In the study of the characteristics of predicted uncertainties, we find that generally more accurate prediction of the bounding box is accompanied by lower uncertainty. The distribution of corner uncertainties agrees on the distribution of the point cloud in the bounding box, which means the corner with denser observed points has lower uncertainty. Moreover, our method learns the constraint from the cuboid geometry of the bounding box in the uncertainty prediction. Finally, we propose an efficient Bayesian updating method to recover the uncertainty for the original parameters of the bounding boxes which can help provide probabilistic results for the tracking and planning module.