The global climate has undergone great changes in recent decades, which has a significant impact on the vegetation system, especially in arid and semi-arid areas. Based on a dynamic model, this paper studied the response of vegetation pattern to climate change in Qinghai Lake, a typical semi-arid region. The conditions for Turing instability of the equilibrium were obtained by mathematical analysis. The numerical experiments showed the influence of different climitic factors (carbon dioxide concentrations [ $C{O}_2$], temperature and precipitation) on vegetation pattern. The results showed that the robustness of the vegetation system was enhanced as precipitation or [ $C{O}_2$] increased. Furthermore, we presented evolution of vegetation system under different climate scenarios to forecast the future growth of vegetation. We compared the various climate scenarios with representative concentration pathways (RCP2.6, RCP4.5, RCP8.5). The results revealed that RCP2.6 scenario was a desired climate scenario for Qinghai Lake. Our study also highlighted the measures to avoid desertification by the method of optimal control. We expect that this study will provide theoretical basis for vegetation protection.