Graph Neural Network （GNN） is increasingly applied to complex fluid system predictions due to the superior capability in handling structured grids and strong combinatorial generalization. However， from a Lagrangian mesh-free perspective， GNN has unpredictable output variations when processing fluid particle information subjected to translation， rotation， or reflection transformations. To address this problem， an Equivariant Graph Neural Network-based Simulator （EGNS） method was proposed. Geometric vectors were first converted into relative equivariants. Then， equivariant message passing was employed at each step to ensure equivariance of entire neural network， maintaining consistency of spatial transformations between output and input equivariants. Finally， the optimized EGNS model was obtained by training in particle trajectories simulated with the Smoothed Particle Hydrodynamics （SPH） method. Experimental results on public fluid simulation datasets demonstrate that EGNS has superior predictive performance compared with Graph Neural Network-based Simulator （GNS）； specifically， EGNS achieves better accuracy in predicting fluid particle movement， velocity， and typical details， decreasing Mean Squared Error （MSE） in predicting particle positions by about 16%.