Cardiac magnetic resonance imaging (MRI) provides 3D images with high-resolution in-plane information, however, they are known to have low through-plane resolution due to the trade-off between resolution, image acquisition time and signal-to-noise ratio. This results in anisotropic 3D images which could lead to difficulty in diagnosis, especially in late gadolinium enhanced (LGE) cardiac MRI which is the reference imaging modality for locating the extent of fibrosis in various cardiovascular diseases like myocardial infarction and atrial fibrillation. To address this issue, we propose a self-supervised deep learning-based approach to enhance the through-plane resolution of the LGE MRI images. We train a convolutional neural network (CNN) model on randomly extracted patches of short-axis LGE MRI images and this trained CNN model is used to leverage the information learnt from the high-resolution in-plane data to improve the through-plane resolution. We conducted experiments on LGE MRI dataset made available through the 2018 atrial segmentation challenge. Our proposed method achieved a mean peak signal-to-noise-ratio (PSNR) of 36.99 and 35.92 and a mean structural similarity index measure (SSIM) of 0.9 and 0.84 on training the CNN model using low-resolution images downsampled by a scale factor of 2 and 4, respectively.