Implicit neural representation gains popularity in modeling the continuous 3D surface for 3D representation and reconstruction. In this work, we are motivated by the fact that the local 3D patches repeatedly appear on 3D shapes/surfaces if removing the factor of poses. Based on this observation, we propose the 3D patch-level equivariant implicit function (PEIF) based on the 3D patch-level pose-invariant representation, allowing us to reconstruct 3D surfaces by estimating equivariant displacement vector fields for query points. Specifically, our model is based on the pose-normalized query/patch pairs and enhanced by the proposed intrinsic patch geometry representation, modeling the intrinsic 3D patch geometry feature by learnable multi-head memory banks. Extensive experiments show that PEIF achieves state-of-the-art performance on multiple surface reconstruction datasets, and also exhibits better generalization to cross-dataset shapes and robustness to arbitrary rotations.