Recently, 3D object detection technology based on point clouds has developed rapidly. However, too few points of distant and occluded objects are scanned by the sensor, and thus these objects suffer from too insufficient features to be detected. This case damages the detection accuracy. Therefore, we constitute a novel 3D object detection with Context-aware and dimensional Interaction Attention Network (CIANet) to explore vital geometric cues for enriching the feature representation of the object, thus boosting the overall detection performance. Specifically, in the first stage, we employ the 3D sparse convolution to extract voxel features, and then construct a Channel-Spatial Hybrid Attention (CSHA) module and a Contextual Self-Attention (CSA) module to enhance voxel features for generating proposals. The CSHA module aims to enhance the key information of the channel and spatial domains of 2D Bird’s Eye View (BEV) features, and the CSA module is applied to supplement contextual information to the enhanced BEV features, thus generating accurate proposals. In the second stage, we construct a Dimensional Interaction Attention (DIA) module to refine Region of Interest (RoI) features within the proposals. It enhances the interactions among the channel and spatial dimensions of RoI features to learn accurate boundaries of objects for proposal refinement. Extensive experiments on the KITTI and Waymo benchmarks show the superior detection performance of CIANet compared to recent methods, especially for objects such as pedestrians and cyclists.