Objective: Accelerated magnetic resonance (MR) image acquisition with compressed sensing (CS) and parallel imaging is a powerful method to reduce MR imaging scan time. However, many reconstruction algorithms have high computational costs. To address this, we investigate deep residual learning networks to remove aliasing artifacts from artifact corrupted images. Methods: The deep residual learning networks are composed of magnitude and phase networks that are separately trained. If both phase and magnitude information are available, the proposed algorithm can work as an iterative k-space interpolation algorithm using framelet representation. When only magnitude data are available, the proposed approach works as an image domain postprocessing algorithm. Results: Even with strong coherent aliasing artifacts, the proposed network successfully learned and removed the aliasing artifacts, whereas current parallel and CS reconstruction methods were unable to remove these artifacts. Conclusion: Comparisons using single and multiple coil acquisition show that the proposed residual network provides good reconstruction results with orders of magnitude faster computational time than existing CS methods. Significance: The proposed deep learning framework may have a great potential for accelerated MR reconstruction by generating accurate results immediately.