In this paper a novel, to the best of our knowledge, deep neural network (DNN), VUR-Net, is proposed to realize direct and accurate phase unwrapping. The VUR-Net employs a relatively large number of filters in each layer and adopts alternately two types of residual blocks throughout the network, distinguishing it from the previously reported ones. The proposed method enables the wrapped phase map to be unwrapped precisely without any preprocessing or postprocessing operations, even though the map has been degraded by various adverse factors, such as noise, undersampling, deforming, and so on. We compared the VUR-Net with another two state-of-the-art phase unwrapping DNNs, and the corresponding results manifest that our proposal markedly outperforms its counterparts in both accuracy and robustness. In addition, we also developed two new indices to evaluate the phase unwrapping. These indices are proved to be effective and powerful as good candidates for estimating the quality of phase unwrapping.