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Detection and tracking of moving objects is an essential component in environmental perception for autonomous driving. In the flourishing field of multi-view 3D camera-based detectors, different transformer-based pipelines are designed to learn queries in 3D space from 2D feature maps of perspective views, but the dominant dense BEV query mechanism is computationally inefficient. This paper proposes Sparse R-CNN 3D (SRCN3D), a novel two-stage fully-sparse detector that incorporates sparse queries, sparse attention with box-wise sampling, and sparse prediction. SRCN3D adopts a cascade structure with the twin-track update of both a fixed number of query boxes and latent query features. Our novel sparse feature sampling module only utilizes local 2D region of interest (RoI) features calculated by the projection of 3D query boxes for further box refinement, leading to a fully-convolutional and deployment-friendly pipeline. For multi-object tracking, motion features, query features and RoI features are comprehensively utilized in multi-hypotheses data association. Extensive experiments on nuScenes dataset demonstrate that SRCN3D achieves competitive performance in both 3D object detection and multi-object tracking tasks, while also exhibiting superior efficiency compared to transformer-based methods. Code and models are available at https://github.com/synsin0/SRCN3D.