In recent years, 4D medical image involving structural and motion information of tissue has attracted increasing attention. The key to the 4D image reconstruction is to stack the 2D slices based on matching the aligned motion states. In this study, the distribution of the 2D slices with the different motion states is modeled as a manifold graph, and the reconstruction is turned to be the graph alignment. An embedding-alignment fusion-based graph convolution network (GCN) with a mixed-learning strategy is proposed to align the graphs. Herein, the embedding and alignment processes of graphs interact with each other to realize a precise alignment with retaining the manifold distribution. The mixed strategy of self- and semi-supervised learning makes the alignment sparse to avoid the mismatching caused by outliers in the graph. In the experiment, the proposed 4D reconstruction approach is validated on the different modalities including Computed Tomography (CT), Magnetic Resonance Imaging (MRI), and Ultrasound (US). We evaluate the reconstruction accuracy and compare it with those of state-of-the-art methods. The experiment results demonstrate that our approach can reconstruct a more accurate 4D image.