Computational simulation of chemical and biological systems using ab initio molecular dynamics has been a challenge over decades. Researchers have attempted to address the problem with machine learning and fragmentation-based methods. However, the two approaches fail to give a satisfactory description of long-range and many-body interactions, respectively. Inspired by fragmentation-based methods, we propose the Long-Short-Range Message-Passing (LSR-MP) framework as a generalization of the existing equivariant graph neural networks (EGNNs) with the intent to incorporate long-range interactions efficiently and effectively. We apply the LSR-MP framework to the recently proposed ViSNet and demonstrate the state-of-the-art results with up to 40% MAE reduction for molecules in MD22 and Chignolin datasets. Consistent improvements to various EGNNs will also be discussed to illustrate the general applicability and robustness of our LSR-MP framework. The code for our experiments and trained model weights could be found at https://github.com/liyy2/LSR-MP.