Ultrasound offers a safe, non-invasive, and inexpensive way of imaging. However, due to its natural intrinsic imaging characteristics, it produces poor quality images with low resolution (LR) compared to other medical imaging modalities. Various image enhancement techniques have been extensively studied to overcome these shortcomings. Super-resolution (SR) is one of these methods, which endeavor to obtain high resolution (HR) images from LR images while enlarging them. Numerous studies have already utilized different SR techniques in various stages of ultrasound imaging (USI). Unlike other studies, which aimed at obtaining SR in the pre-processing phase or early stages of the post-processing phase of USI, we achieved SR on B-mode ultrasound images, which is the last stage of USI. We constructed a deep convolutional neural network (CNN) and trained it with a very large dataset of B-mode ultrasound images for the scale factors 2, 3, 4, and 8. We evaluated the performance of our proposed model quantitatively with eight image quality measures. The quantitative results revealed that our algorithm is much more successful than other methods at each magnification factor. Furthermore, we also verified that there is a statistically significant difference between our approach and others. Besides, qualitative analysis of the reconstructed images also confirms that it produces much better quality HR images than other methods in terms of the human visual system.