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Magnetic resonance image (MRI) in high spatial resolution provides detailed anatomical information and is often necessary for accurate quantitative analysis. However, high spatial resolution typically comes at the expense of longer scan time, less spatial coverage, and lower signal to noise ratio (SNR). Single Image Super-Resolution (SISR), a technique aimed to restore high-resolution (HR) details from one single low-resolution (LR) input image, has been improved dramatically by recent breakthroughs in deep learning. In this paper, we introduce a new neural network architecture, 3D Densely Connected Super-Resolution Networks (DCSRN) to restore HR features of structural brain MR images. Through experiments on a dataset with 1,113 subjects, we demonstrate that our network outperforms bicubic interpolation as well as other deep learning methods in restoring 4× resolution-reduced images.