High-resolution diffusion imaging with submillimeter isotropic voxels requires long scan times that are usually clinically impractical. Even with those long scans, the image quality can still suffer from low signal-to-noise ratio (SNR) and severe geometric distortion due to long echo spacing in echo-planar imaging sequences. In this study, we proposed and validated the efficacy of using a state-of-the-art deep-learning method, super-resolution convolutional neural network (SRCNN), to achieve submillimeter super-resolution diffusion-weighted (DW) images. The 2D-based deep-learning method was validated by comparing with the ground truth using numerical simulations and by studying region-of-interest (ROI) using real human data of three healthy volunteers. Furthermore, we interrogated the proposed method under different real-life SNR conditions. The results demonstrated that the proposed deep-learning method was able to reproduce sufficient details in the anatomy that can only be detected using high-resolution diffusion imaging. The percentage errors in diffusion tensor imaging (DTI) derived metrics were less than 8% when the baseline SNR larger than 20. The ROI results demonstrated that the proposed method produced comparable values of diffusion metrics to the matched high-resolution diffusion metrics of real human data. Particularly, the patterns of distributions of the subjects were similar between the proposed method and real data across whole-brain gray-matter and white-matter ROIs. A deep-learned submillimeter resolution of 0.625 mm diffusion directional image showed high image quality, particularly in the cortical gray matter. We demonstrated the feasibility of using a deep-learning algorithm based on SRCNN in DTI. This approach can be a robust alternative when acquiring the true sub-millimeter diffusion MRI is not available.