This paper proposes GCGM, an end-to-end framework integrating graph convolutional networks and graph matching to estimate left ventricular (LV) motion from cardiac MR images. Key innovations include a triangulation-based graph construction method that preserves LV contour topology and a cross-graph feature propagation mechanism using learnable similarity matrices. A doubly stochastic loss refines correspondences, while compact support radial basis functions generate smooth deformation fields between cardiac phases. Evaluated on the York and MICCAI 2009 datasets, GCGM achieves 97.4% average accuracy in point matching and superior deformation smoothness (mean Jacobian number: 30.1), outperforming existing methods in robustness to complex deformations, demonstrating its potential for precise cardiac motion analysis.