There is an emphasis on urban carbon peaking in the building industry, and public buildings (PB) are the major source of building industry carbon emissions. This research develops a model for forecasting PB’s carbon emissions in Shanxi Province by using the LEAP model to analyze the carbon peaking time and carbon emission level under various scenarios for PB in Shanxi Province in 2021–2050. The findings indicate that: (1) The baseline scenario and the control area scenario do not reach the peak during the forecast period; the energy-saving scenario is synchronized with China’s peak carbon target to peak in 2030; the green scenario is the optimal scenario set in this research and reaches the peak in 2025. (2) Controlling the public building area moderately can decrease carbon emissions and energy consumption to a great extent. (3) Carbon emissions can be reduced and peak times brought forward by reducing energy intensity, adjusting the energy structure, cleaning the heat network, and cleaning the grid. Finally, according to the prediction results, the carbon peak path of PB in Shanxi Province provides useful references for public building carbon emission reduction in the mid-latitude inland areas.