The morphological changes in mountain glaciers are effective in indicating the environmental climate change in the alpine ice sheet. Aiming at the problems of single monitoring index and low prediction accuracy of mountain glacier deformation at present, this study takes Meili Mountain glacier in western China as the research object and uses InSAR technology to construct the mountain glacier deformation time series and 3D deformation field from January 2020 to December 2021. The relationship between glacier deformation and elevation, slope, aspect, glacier albedo, surface organic carbon content, and rainfall was revealed by grey correlation analysis. The GA-BP neural network prediction model is established from the perspective of multiple factors to predict the deformation of Meili Mountain glacier. The results showed that: The deformation of Meili Mountain glacier has obvious characteristics of spatio-temporal differentiation; the cumulative maximum deformation quantity of glaciers in the study period is −212.16 mm. After three-dimensional decomposition, the maximum deformation quantity of glaciers in vertical direction, north–south direction and east–west direction is −125.63 mm, −77.03 mm, and 107.98 mm, respectively. The average annual deformation rate is between −94.62 and 75.96 mm/year. The deformation of Meili Mountain glacier has a gradient effect, the absolute value of deformation quantity is larger when the elevation is below 4500 m, and the absolute value of deformation quantity is smaller when it is above 4500 m. The R2, MAPE, and RMSE of the GA-BP neural network to predict the deformation of Meili glacier are 0.86, 1.12%, and 10.38 mm, respectively. Compared with the standard BP algorithm, the prediction accuracy of the GA-BP neural network is significantly improved, and it can be used to predict the deformation of mountain glaciers.