Typical Magnetic Resonance Imaging (MRI) scan may take 20 to 60 minutes. Reducing MRI scan time is beneficial for both patient experience and cost considerations. Accelerated MRI scan may be achieved by acquiring less amount of k-space data (down-sampling in the k-space). However, this leads to lower resolution and aliasing artifacts for the reconstructed images. There are many existing approaches for attempting to reconstruct high-quality images from down-sampled k-space data, with varying complexity and performance. In recent years, deep-learning approaches have been proposed for this task, and promising results have been reported. Still, the problem remains challenging especially because of the high fidelity requirement in most medical applications employing reconstructed MRI images. In this work, we propose a deep-learning approach, aiming at reconstructing high-quality images from accelerated MRI acquisition. Specifically, we use Convolutional Neural Network (CNN) to learn the differences between the aliased images and the original images, employing a U-Net-like architecture. Further, a micro-architecture termed Residual Dense Block (RDB) is introduced for learning a better feature representation than the plain U-Net. Considering the peculiarity of the downsampled k-space data, we introduce a new term to the loss function in learning, which effectively employs the given k-space data during training to provide additional regularization on the update of the network weights. To evaluate the proposed approach, we compare it with other state-of-the-art methods. In both visual inspection and evaluation using standard metrics, the proposed approach is able to deliver improved performance, demonstrating its potential for providing an effective solution.