Multi-contrast images in magnetic resonance imaging (MRI) are widely applied in clinical applications, since an abundant contrast information reflects the characteristics of the internal tissue of human body, providing an effective reference for clinical diagnosis. However, long acquisition time limits the application of magnetic resonance multi contrast imaging. Under-sampling the k-space data and reconstructing images with sparsity constraint is one efficient way to accelerate magnetic resonance imaging sampling. In this work, multi-contrast undersampled MRI images are jointly reconstructed under the sparse representation using graph wavelets. Experiment results demonstrate that the proposed method outperforms the compared state-of-the-art methods.