The key step of optical interferometry is phase unwrapping， which is expected to be computationally fast， highly precise， and widely applicable. According to the feature of wrapped phase that between different order fringes there are significant edges, a fast unwrapping algorithm based on region segmenting with mathematical morphology(RSMM) is proposed. First， mathematical morphology is applied to extract the boundaries and segment regions from the phase map. Then, phase differences between adjacent regions are calculated in order to determine the phase order and elevated quantity of each region, and so are phases of the pixels on boundaries. Finally， wrapped phases in regions and boundaries are elevated individually according to the quantified elevation to obtain the unwrapped phase map. Simulations and experiments indicate that RSMM requires less than 1 second to unwrap and generate a phase map for 1 000×1 000 pixels， and this required time is less than a quarter of the computation time of conventional least-square algorithms. In addition， the phase unwrapping performance is not influenced by phase boundary， data dropout， and noise. The RSMM algorithm has the advantages of high speed， broad adaptability， and high accuracy and is promising for measurement applications with a commanding requirement for computation speed， such as dynamic interferometry， optical holography， and fringe projecting profilometry.