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This paper presents a new phase unwrapping algorithm based on the unscented Kalman filter (UKF) for synthetic aperture radar (SAR) interferometry. This method is the result of combining an UKF with path-following strategy and an omni-directional local phase slope estimator. This technique performs simultaneously noise filtering and phase unwrapping along the high-quality region to the low-quality region, which is also able to avoid going directly through the noisy regions. In addition, phase slope is estimated directly from the sample frequency spectrum of the complex interferogram, by which the underestimation of phase slope is overcome. Simulation and real data processing results validate the effectiveness of the proposed method, and show a significant improvement with respect to the extended Kalman filtering (EKF) algorithm and some conventional phase unwrapping algorithms in some situations.