For the prevention of the stack effect in high-rise buildings in winter, this paper studied a method to cool the shaft by natural ventilation through the opening between the shaft and out air. It was shown theoretically that the shaft is effectively cooled by putting the opening in the lower level of the shaft and thus the stack effect can be effectively prevented. By the calculation for a high-rise building based on the airflow network model and the steady heat balance analysis, it was shown quantitatively that the studied method is effective for general high-rise office buildings and that a careful survey is necessary before introducing this method for the following cases: 1)a case in which the down flow occur in the shaft influenced by the existence of another shaft, 2)a case in which there is no opening to the outside in the upper level of the shaft, 3)a case in which the humidity of the building is high.