GPS uses the radio signals transmitted by satellites to determine the position of the user receiver on the earth by calculating the relative position between the satellite and the GPS receiver, and can provide real-time positioning, speed measurement and timing services for the user receiver. By using the least squares method, the GPS positioning solution algorithm is studied, and a GPS positioning solution algorithm based on the least squares method is designed in the paper. The designed GPS positioning algorithm is verified by the positioning solution test by using the simulated source, and the positioning solution result is compared with the set position of the simulated receiver. The test results show that the positioning solution algorithm has a good positioning effect.