Though 3D object detection from point clouds has achieved rapid progress in recent years, the lack of flexible and high-performance proposal refinement remains a great hurdle for existing state-of-the-art two-stage detectors. Previous works on refining 3D proposals have relied on human-designed components such as keypoints sampling, set abstraction and multi-scale feature fusion to produce powerful 3D object representations. Such methods, however, have limited ability to capture rich contextual dependencies among points. In this paper, we leverage the high-quality region proposal network and a Channel-wise Transformer architecture to constitute our two-stage 3D object detection framework (CT3D) with minimal hand-crafted design. The proposed CT3D simultaneously performs proposal-aware embedding and channel-wise context aggregation for the point features within each proposal. Specifically, CT3D uses proposal's keypoints for spatial contextual modelling and learns attention propagation in the encoding module, mapping the proposal to point embeddings. Next, a new channel-wise decoding module enriches the query-key interaction via channel-wise re-weighting to effectively merge multi-level contexts, which contributes to more accurate object predictions. Extensive experiments demonstrate that our CT3D method has superior performance and excellent scalability. Remarkably, CT3D achieves the AP of 81.77% in the moderate car category on the KITTI test 3D detection benchmark, outperforms state-of-the-art 3D detectors.