We present a new 3D point-based detector model, named Shift-SSD, for precise 3D object detection in autonomous driving. Traditional point-based 3D object detectors often employ architectures that rely on a progressive downsampling of points. While this method effectively reduces computational demands and increases receptive fields, it will compromise the preservation of crucial non-local information for accurate 3D object detection, especially in the complex driving scenarios. To address this, we introduce an intriguing Cross-Cluster Shifting operation to unleash the representation capacity of the point-based detector by efficiently modeling longer-range inter-dependency while including only a negligible overhead. Concretely, the Cross-Cluster Shifting operation enhances the conventional design by shifting partial channels from neighboring clusters, which enables richer interaction with non-local regions and thus enlarges the receptive field of clusters. We conduct extensive experiments on the KITTI, Waymo, and nuScenes datasets, and the results demonstrate the state-of-the-art performance of Shift-SSD in both detection accuracy and runtime efficiency.