Current phase-unwrapping algorithms are generally challenged by severe noise, rapid-varying phase or disconnected regions. We present a novel phase-unwrapping method by using phase jumps detection and local polynomial surface fitting. The proposed method first segments the whole phase map into blocks by exploiting the phase jumps that are automatically identified. Intra-block wrapping may still exist if the true phase difference between adjacent pixels exceeds π inside a block. To address potential intra-block wraps, we further segment each block into subblocks using the phase partition method, and perform inter-subblock unwrapping using the block-growing method. Simulation and in vivo Dixon water-fat separation experiments were implemented to evaluate the performance of the proposed method, with comparisons to PRELUDE and CLOSE. This method has great potential in phase-related MRI applications in practice.