Pumping airflow occurs in single-sided natural ventilation buildings when the openings are located on the leeward side; the direction of airflow through the building then changes periodicity. In order to propose a calculation method of the ventilation rates for single-room buildings and analyze the pumping ventilation for multi-room buildings, the CFD method with an SST k-ω turbulence model was used to conduct numerical simulation in this study, which is verified by other experimental results. Firstly, the qualitative and quantitative characteristics of pumping ventilation were investigated for a single-room building with two openings. The results show that the steady-state method underestimates the ventilation flow rates, and the unsteady-state method captures the microstructures of the flow better. Secondly, the vortex-shedding and indoor airflow oscillation frequencies were analyzed based on transient simulation for a single-room building. It was found that both of them increase with air speed. Then, the factors affecting ventilation flow rates were analyzed. A calculation method for dimensionless ventilation rates is proposed. Finally, the pumping ventilation for a multi-room building was numerically simulated. The ventilation rate for a middle room is greater than that for a corner room, and the ventilation rate for any room in a multi-room building is greater than the single-room building given the same room size and the same incoming wind speed. The findings of this paper are helpful for the design and evaluation of natural ventilation.