Gross primary productivity (GPP) is an important indicator in research on carbon cycling in terrestrial ecosystems. High-accuracy GPP prediction is crucial for ecosystem health and climate change assessments. We developed a site-level GPP prediction method based on the GeoMAN model, which was able to extract spatiotemporal features and fuse external environmental factors to predict GPP on the Tibetan Plateau. We evaluated four models’ behavior—Random Forest (RF), Support Vector Machine (SVM), Deep Belief Network (DBN), and GeoMAN—in predicting GPP at nine flux observation sites on the Tibetan Plateau. The GeoMAN model achieved the best results (R² = 0.870, RMSE = 0.788 g Cm⁻² d⁻¹, MAE = 0.440 g Cm⁻² d⁻¹). Distance and vegetation type of the flux sites influenced GPP prediction, with the latter being more significant. The different grassland vegetation types exhibited different sensitivity to environmental factors (Ta, PAR, EVI, NDVI, and LSWI) for GPP prediction. Among them, the site located in the alpine swamp meadow was insensitive to changes in environmental factors; the GPP prediction accuracy of the site located in the alpine meadow steppe decreased significantly with the changes in environmental factors; and the GPP prediction accuracy of the site located in the alpine Kobresia meadow also varied with environmental factor changes, but to a lesser extent than the former. This study provides a good reference that deep learning model is able to achieve good accuracy in GPP simulation when considers spatial, temporal, and environmental factors, and the judgement made by deep learning model conforms to basic knowledge in the relevant field.