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Magnetic resonance imaging (MRI) with high resolution (HR) provides more detailed information for accurate diagnosis and quantitative image analysis. Despite the significant advances, most existing super-resolution (SR) reconstruction network for medical images has two flaws: 1) All of them are designed in a black-box principle, thus lacking sufficient interpretability and further limiting their practical applications. Interpretable neural network models are of significant interest since they enhance the trustworthiness required in clinical practice when dealing with medical images. 2) most existing SR reconstruction approaches only use a single contrast or use a simple multi-contrast fusion mechanism, neglecting the complex relationships between different contrasts that are critical for SR improvement. To deal with these issues, in this paper, a novel Model-Guided interpretable Deep Unfolding Network (MGDUN) for medical image SR reconstruction is proposed. The Model-Guided image SR reconstruction approach solves manually designed objective functions to reconstruct HR MRI. We show how to unfold an iterative MGDUN algorithm into a novel model-guided deep unfolding network by taking the MRI observation matrix and explicit multi-contrast relationship matrix into account during the end-to-end optimization. Extensive experiments on the multi-contrast IXI dataset and BraTs 2019 dataset demonstrate the superiority of our proposed model.