High resolution magnetic resonance (MR) imaging (MRI) is desirable in many clinical applications; however, there is a trade-off between resolution, speed of acquisition, and noise. It is common for MR images to have worse through-plane resolution (slice thickness) than in-plane resolution. In these MRI images, high frequency information in the through-plane direction is not acquired, and cannot be resolved through interpolation. To address this issue, super-resolution methods have been developed to enhance spatial resolution. As an ill-posed problem, state-of-the-art super-resolution methods rely on the presence of external/training atlases to learn the transform from low resolution (LR) images to high resolution (HR) images. For several reasons, such HR atlas images are often not available for MRI sequences. This paper presents a self super-resolution (SSR) algorithm, which does not use any external atlas images, yet can still resolve HR images only reliant on the acquired LR image. We use a blurred version of the input image to create training data for a state-of-the-art super-resolution deep network. The trained network is applied to the original input image to estimate the HR image. Our SSR result shows a significant improvement on through-plane resolution compared to competing SSR methods.