Considering data reliability, the optimized connections of dual residues for phase discontinuity reconstruction provide a more reliable scheme and produce more robust unwrapped results. However, their practical implementation usually involves a time-consuming iterative global operation, which is not suitable for application to the phase unwrapping (PU) of big blocks of interferometric synthetic aperture radar (InSAR) phase data. A parallel PU method based on local minimum reliability dual expanding is proposed. With given quality weight maps, the dual reliability is defined based on residues, and the minimum reliability residue pairs are introduced to represent possible discontinuous boundaries. We provide a dynamic expanding method for the pairs with local minimum reliability searching and dual merging. The final minimum balanced trees obtained are used for path integrating of PU with the aid of reliability maps. The calculation of reliability maps, the residue pair searching, and the dynamic expanding are designed to be carried out in parallel. We employ the interface propagation scheme based on the eikonal equation and flood-filling for the parallel implement. Two big blocks of airborne InSAR data were processed by the proposed method, the experimental results and analysis verified its robustness and efficiency for the large-scale PU problem.