Two-dimensional phase unwrapping algorithms are widely used in optical metrology and measurements. The high noise from interference measurements, however, often leads to the failure of conventional phase unwrapping algorithms. In this paper, we propose a deep convolutional neural network (DCNN) based method to perform rapid and robust two-dimensional phase unwrapping. In our approach, we employ a DCNN architecture, DeepLabV3+, with noise suppression and strong feature representation capabilities. The employed DCNN is first used to perform semantic segmentation to obtain the segmentation result of the wrapped phase map. We then combine the wrapped phase map with the segmentation result to generate the unwrapped phase. We benchmarked our results by comparing them with well-established methods. The reported approach out-performed the conventional path-dependent and path-independent algorithms. We also tested the robustness of the reported approach using interference measurements from optical metrology setups. Our results, again, clearly out-performed the conventional phase unwrap algorithms. The reported approach may find applications in optical metrology and microscopy imaging.