Changes of grazing pressure and climate have been identified as drivers of woody encroachment in subalpine pastures, but disentangling their relative importance remains challenging. It is particularly unclear if grazing alone can mitigate potential climate change impacts on encroachment. We used the dynamic vegetation model LandClim to simulate how multiple biotic and abiotic factors influence the rate of woody encroachment (i.e. how changes in temperature and precipitation influence woody and herbaceous vegetation, and interactions with grazing). We simulated a 61-ha subalpine pasture in Switzerland near tree line. Currently, 21% of the pasture is covered by woody plants. If current grazing levels are maintained, almost all climate change scenarios showed an increase in woody cover. Under the RCP 4.5 and RCP 8.5 scenarios, there was a mean encroachment rate of 0.24% and 0.15% per year respectively. Large variation among climate model chains with RCP 8.5 was found, due to variations in precipitation. Generally, decreasing precipitation caused woody encroachment to slow down, even under very low grazing pressures. Using a sensitivity analysis with all possible combinations of grazing pressure, temperature and precipitation changes, we found that woody encroachment rates were most sensitive to changes in grazing pressure. Precipitation change was the second most important factor, while temperature changes were least important. Synthesis and applications. Modelling shows that increasing grazing pressure in subalpine pastures can strongly reduce woody encroachment and mitigate climate change impacts on woody encroachment.