More and more research works fuse the LiDAR and camera information to improve the 3D object detection of the autonomous driving system. Recently, a simple yet effective fusion framework has achieved an excellent detection performance, fusing the LiDAR and camera features in a unified bird's-eye-view (BEV) space. In this paper, we propose a LiDAR-camera fusion framework, named SimpleBEV, for accurate 3D object detection, which follows the BEV-based fusion framework and improves the camera and LiDAR encoders, respectively. Specifically, we perform the camera-based depth estimation using a cascade network and rectify the depth results with the depth information derived from the LiDAR points. Meanwhile, an auxiliary branch that implements the 3D object detection using only the camera-BEV features is introduced to exploit the camera information during the training phase. Besides, we improve the LiDAR feature extractor by fusing the multi-scaled sparse convolutional features. Experimental results demonstrate the effectiveness of our proposed method. Our method achieves 77.6\% NDS accuracy on the nuScenes dataset, showcasing superior performance in the 3D object detection track.