C‐band Interferometric Synthetic Aperture Radar (InSAR) data are widely used to map coseismic deformation. However, phase unwrapping errors are commonly distributed near faults owing to decorrelation and steep phase gradients from short radar wavelengths. Here, we propose an improved SNAPHU phase‐unwrapping algorithm that considers the prior information of the range offset gradients (P‐SNAPHU) to overcome the constraints imposed by the phase continuity assumption. P‐SNAPHU exploits median filtering of homogeneous pixels for initial denoising of range offset and then refines range offset gradients divisionally through saliency extraction. The derived gradients are used to estimate the expected values of the cost functions for the low‐coherence fringes. The synthetic experiments show significant improvements in the phase‐unwrapping accuracy of the P‐SNAPHU method compared with classical unwrapping methods. We apply the P‐SNAPHU method to unwrap Sentinel‐1 coseismic interferograms of three large (Mw > 6.5) strike‐slip earthquake events that the existing classical methods could not successfully unwrap. In the comparison of the unwrapped interferograms with the external global navigation satellite system (GNSS) displacements and those from the classical methods, we find that P‐SNAPHU significantly reduces the phase unwrapping errors with the mean absolute error of 7.2, 2.3, and 1.8 cm for the 2023 Kahramanmaraş earthquake doublet, the 2016 Kumamoto earthquake, and the 2019 Ridgecrest earthquakes, respectively. Based on the unwrapped results derived from P‐SNAPHU, an estimate is made regarding the shallow slip deficit of the 2023 Kahramanmaraş earthquake doublet, which is approximately 7%. Therefore, P‐SNAPHU is useful for developing and applying C‐band InSAR data for large earthquakes and volcanic activity.