Underground mining operations may lead to extensive surface environmental issues such as ground subsidence, cracks, and water accumulation. Obtaining high-precision mining subsidence prediction parameters in advance allows for accurate prediction of ground subsidence, which is of great significance for protecting the ecological environment and preventing geological disasters in mines. Currently, methods for obtaining subsidence prediction parameters based on surface measurement data primarily rely on inversion algorithms. However, these algorithms are often susceptible to outliers, resulting in low robustness and consequently limiting the accuracy of the predicted results. To address this issue, this study presents the RANSAC-DE algorithm, which integrates the high precision, efficiency, and global search capabilities of the Differential Evolution (DE) algorithm with the high robustness of the Random Sample Consensus (RANSAC) algorithm. The comparison of simulation experiments shows that the RANSAC-DE algorithm can effectively identify and eliminate the interference of outliers, and its anti-outlier interference performance is much better than DE and Huber-DE. In addition, the RANSAC-DE algorithm inherits the advantages of the DE algorithm, such as high inversion accuracy, strong global search capability, robustness against missing observation points interference, and Gaussian noise interference. The measured data of the 1312 working face of Guqiao Mine was used for case verification. The root mean square error (RMSE) of the subsidence fitting obtained by the RANSAC-DE method is 33.2 mm, much better than the 62.2 mm and 67.6 mm obtained by the DE and Huber-DE methods, respectively. Furthermore, ML06, ML07, and ML09 are correctly identified as outliers, verifying the robustness of the RANSAC-DE algorithm.