Super-resolution (SR) MR image reconstruction has shown to be a very promising direction to improve the spatial resolution of low-resolution (LR) MR images. In this paper, we presented a novel MR image SR method based on a dense convolutional neural network (DDSR), and its enhanced version called EDDSR. There are three major innovations: first, we re-designed dense modules to extract hierarchical features directly from LR images and propagate the extracted feature maps through dense connections. Therefore, unlike other CNN-based SR MR techniques that upsample LR patches in the initial phase, our methods take the original LR images or patches as input. This effectively reduces computational complexity and speeds up SR reconstruction. Second, a final deconvolution filter in our model automatically learns filters to fuse and upscale all hierarchical feature maps to generate HR MR images. Using this, EDDSR can perform SR reconstructions at different upscale factors using a single model with one stride fixed deconvolution operation. Third, to further improve SR reconstruction accuracy, we exploited a geometric self-ensemble strategy. Experimental results on three benchmark datasets demonstrate that our methods, DDSR and EDDSR, achieved superior performance compared to state-of-the-art MR image SR methods with less computational load and memory usage.