This paper proposes a convolutional neural network approach for single-image super-resolution of 3D CT and MRI scans. The method uses two CNNs, with the first increasing resolution on two axes and the second increasing it on the third axis. Unlike other methods, it computes loss with respect to the high-resolution ground truth image after the intermediate upscaling layer, in addition to the final layer. This intermediate loss helps produce outputs closer to the ground truth. It also applies Gaussian smoothing with various standard deviations during training to avoid overfitting. Evaluation on two databases shows the approach achieves superior results compared to interpolation schemes and related works, with human observers preferring its outputs in over 97% of cases for 2x and 4x up