A typical clinical MRI scanning session produces image sets with same geometries but different contrasts. These multi-contrast images often share strong structural similarities or correlations despite their contrast differences. Most existing MRI denoising methods deal with single-contrast images independently, and fail to explore and utilize such correlations across contrasts. In this study, we present a simultaneous denoising method for multi-contrast images based on low rank multi-contrast patch matrix completion. This denoising method exploits the structural similarities across contrasts, and outperforms the traditional method. Further, it does not compromise the image fidelity in absence of any structural similarities across contrasts.