In recent years, Graph Convolutional Networks (GCNs) have been widely used in human motion prediction, but their performance remains unsatisfactory. Recently, MLP-Mixer, initially developed for vision tasks, has been leveraged into human motion prediction as a promising alternative to GCNs, which achieves both better performance and better efficiency than GCNs. Unlike GCNs, which can explicitly capture human skeleton's bone-joint structure by representing it as a graph with edges and nodes, MLP-Mixer relies on fully connected layers and thus cannot explicitly model such graph-like structure of human's. To break this limitation of MLP-Mixer's, we propose \textit{Graph-Guided Mixer}, a novel approach that equips the original MLP-Mixer architecture with the capability to model graph structure. By incorporating graph guidance, our \textit{Graph-Guided Mixer} can effectively capture and utilize the specific connectivity patterns within human skeleton's graph representation. In this paper, first we uncover a theoretical connection between MLP-Mixer and GCN that is unexplored in existing research. Building on this theoretical connection, next we present our proposed \textit{Graph-Guided Mixer}, explaining how the original MLP-Mixer architecture is reinvented to incorporate guidance from graph structure. Then we conduct an extensive evaluation on the Human3.6M, AMASS, and 3DPW datasets, which shows that our method achieves state-of-the-art performance.