In order to realize the engineering application of the branch-cut method in the phase diagram unwrapping of laser speckle pattern interferometry, and to solve the problems of dense branch lines and slow calculation speed caused by the interference of external light, the degradation of laser performance and the undersampling of local points taken by cameras, an optimization and improvement scheme based on Goldstein branch-cut method was proposed. The residual points were regarded as "electrons" with positive and negative unit electric quantities, guided by electromagnetic force, and eliminated by phase smoothing or increasing phase jump, thus reducing the number of branch lines. At the same time, GPU parallel computing technology was adopted to improve the processing speed of high-resolution and large-size phase diagram. The simulation experiment and actual measurement data show that the unwrapping diagram quality is better by the improved branch-cut method. For the 5 million pixel speckle phase diagram, more than 98% of the residual points can be eliminated by electromagnetic force, and the branch lines can be reduced by more than 90%. The processing time can be reduced from the previous 15 seconds to 1.5 seconds, which meets the engineering application requirements of high quality and quick unwrapping by branch-cut method.