In electronic speckle pattern interferometry (ESPI), the true phase is generally extracted by the phasestepping method, which can only get the wrapped phase. Before the phase can be used to provide quantitative information, the wrapped phase must be unwrapped. But ESPI fringe patterns are contaminated with high levels of speckle noise, the task of phase unwrapping remains a challenge. In this article, a novel phase unwrapping algorithm based on graphcuts is proposed, which treats the phase unwrapping problem as integer optimizations. By the method of energy minimization, the novel algorithm can accurately extract the phase from wrapped phase images containing large amount of noise without prefiltering. For the same simulated wrapped speckle phase map,the RMSE(root mean squared error) of the traditional MaskCuts and LeastSquare are respectively 11.707 6 and 4.977 5, while the new algorithm's RMSE is 0.9459.Numerical simulation and experimental results both verify the excellent antinoise performance of the new algorithm.