The field of geometric deep learning has had a profound impact on the development of innovative and powerful graph neural network architectures. Disciplines such as computer vision and computational biology have benefited significantly from such methodological advances, which has led to breakthroughs in scientific domains such as protein structure prediction and design. In this work, we introduce GCPNet, a new geometry-complete, SE(3)-equivariant graph neural network designed for 3D graph representation learning. We demonstrate the state-of-the-art utility and expressiveness of our method on six independent datasets designed for three distinct geometric tasks: protein-ligand binding affinity prediction, protein structure ranking, and Newtonian many-body systems modeling. Our results suggest that GCPNet is a powerful, general method for capturing complex geometric and physical interactions within 3D graphs for downstream prediction tasks. The source code, data, and instructions to train new models or reproduce our results are freely available on GitHub.