Two-dimensional phase unwrapping (2-D PU) is one of the key processes in reconstructing the topography or displacement of the Earth surface from its interferometric synthetic aperture radar (InSAR) data. Estimating the absolute phase gradient information is an unavoidable step utilized by almost all the 2-D PU methods. Traditionally, the gradient estimation step relies on the phase continuity assumption, which requests that the observed area has spatial continuity. However, the abrupt topographic changes and system noise usually results in the failure of the phase continuity assumption in reality. Under this condition, it is difficult for the traditional 2-D PU to provide the correct absolute phase over the area with abrupt interferometric fringe change or with strong system noise. To solve the issue, we propose a novel deep convolutional neural network (DCNN), abbreviated as PGNet, to estimate the phase gradient information instead of the phase continuity assumption in this article. The major advantage of PGNet lies in its deep architecture to learn the characteristics of phase gradients from enormous training images with different noise levels and topographic features. Subsequently, the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm objective function is used to minimize the difference between unwrapped phase gradients and the gradients estimated by PGNet for obtaining the final PU result. Taking the phase gradient pattern of the TerraSAR-X-TanDEM-X interferogram as the learning object, experimental results demonstrate the absolute phase gradient estimated by PGNet is more credible than that from the phase continuity assumption such that the corresponding PU result outperforms those obtained by the traditional 2-D PU methods.