Multi-person pose estimation (MPPE), which aims to locate keypoints for all persons in the frames, is an active research branch of computer vision. Variable human poses and complex scenes make MPPE dependent on both local details and global structures, and the absence of them may cause keypoint feature misalignment. In this case, high-order spatial interactions that can effectively link the local and global information of features are particularly important. However, most methods do not have spatial interactions, and a few methods have low-order spatial interactions but they are difficult to achieve a good balance between accuracy and complexity. To address the above problems, a Dual-Residual Spatial Interaction Network (DRSI-Net) for MPPE with high accuracy and low complexity is proposed in this paper. DRSI-Net recursively performs residual spatial information interactions on neighbor features, so that more useful spatial information can be retained and more similarities can be obtained between shallow and deep extracted features. The channel and spatial dual attention mechanism introduced in the multi-scale feature fusion also helps the network to adaptively focus on features relevant to target keypoints and further refine generated poses. At the same time, by optimizing interactive channel dimensions and dividing gradient flow, the spatial interaction module is designed to be lightweight, which reduces the complexity of the network. According to the experimental results on the COCO dataset, the proposed DRSI-Net outperforms other state-of-the-art methods in both accuracy and complexity.