Magnetic Resonance Imaging (MRI) has been widely used in clinical application and pathology research to help doctors provide better diagnoses. However, accurate diagnosis by MRI remains a great challenge, as images obtained via current MRI techniques usually have low resolutions. Improving MRI image quality and resolution has thus become a critically important task. This paper presents an innovative Coupled-Projection Residual Network (CPRN) for MRI super-resolution. CPRN consists of two complementary sub-networks':' a shallow network and a deep one, which maintain content consistency while learning high frequency differences between low-resolution and high-resolution images. The shallow sub-network employs coupled-projection to better retain the MR image details, where a novel feedback mechanism is introduced to guide the reconstruction of high-resolution images. The deep sub-network learns from the residuals of the high-frequency image information, where multiple residual blocks are cascaded to magnify the MR images at the last network layer. Finally, the features from the shallow and deep sub-networks are fused for the reconstruction of high-resolution MR images. For effective feature fusion between the deep and shallow sub-networks, a step-wise connection (CPRN_S) is designed, inspired by the human cognitive process (from simple to complex). Experiments over three public MRI datasets show that our proposed CPRN achieves superior MRI super-resolution performance compared with the state-of-the-art.