This paper introduces Equivariant Graph Neural Operator (EGNO), a novel method for modeling 3D dynamics by directly learning temporal correlations in trajectories rather than just next-step predictions. EGNO is designed to retain SE(3)-equivariance while learning dynamics as functions over time. The method combines equivariant graph neural networks (EGNNs) with equivariant temporal convolutions in the Fourier domain to model the evolution of 3D systems. EGNO is the first operator learning framework that maintains 3D equivariance while modeling solution dynamics functions over time. The approach is validated across multiple domains, including particle simulations, human motion capture, and molecular dynamics, where it outperforms existing methods significantly. EGNO's key innovation lies in its ability to model dynamics as a function over time, enabling efficient parallel decoding of future states and maintaining geometric equivariance. The framework is general and can be combined with various EGNN layers, making it applicable to a wide range of physical dynamics scenarios. Comprehensive experiments demonstrate that EGNO achieves superior performance in modeling geometric dynamics, with significant improvements over existing methods in terms of accuracy and efficiency. The method is implemented in code available at https://github.com/MinkaiXu/egno.This paper introduces Equivariant Graph Neural Operator (EGNO), a novel method for modeling 3D dynamics by directly learning temporal correlations in trajectories rather than just next-step predictions. EGNO is designed to retain SE(3)-equivariance while learning dynamics as functions over time. The method combines equivariant graph neural networks (EGNNs) with equivariant temporal convolutions in the Fourier domain to model the evolution of 3D systems. EGNO is the first operator learning framework that maintains 3D equivariance while modeling solution dynamics functions over time. The approach is validated across multiple domains, including particle simulations, human motion capture, and molecular dynamics, where it outperforms existing methods significantly. EGNO's key innovation lies in its ability to model dynamics as a function over time, enabling efficient parallel decoding of future states and maintaining geometric equivariance. The framework is general and can be combined with various EGNN layers, making it applicable to a wide range of physical dynamics scenarios. Comprehensive experiments demonstrate that EGNO achieves superior performance in modeling geometric dynamics, with significant improvements over existing methods in terms of accuracy and efficiency. The method is implemented in code available at https://github.com/MinkaiXu/egno.