In order to improve the measurement accuracy of the elliptical Gaussian spot position in the four quadrant detector and the position detection accuracy of the elliptical spot and the center coordinate of the four quadrant detector with an offset rotation angle, a localization algorithm for the elliptical Gaussian spot is proposed. An elliptical light spot with Gaussian distribution was used as the incident light spot model, and infinite integral fitting algorithm and the least squares method were used to fit the optimal analytical expression. In order to establish all models of elliptical spot in the four quadrant detector, polynomial fitting was performed on the offset angle to simplify the calculation of the algorithm for locating the offset angle between the elliptical spot and the center coordinate of the four quadrant detector. Finally, based on simulation, the fitting relationship between the offset angle and the localization algorithm was determined. The positioning accuracy of the algorithm can reach sub-micron level, providing a theoretical basis for the localization algorithm of elliptical spots.