The geometric characteristics of the building have an important effect on the initiation of the upward leader. Based on a three-dimensional variable grid physical lightning model, in the case of buildings with different geometric characteristics and the peak current of the lightning strike (IP), the influence factors of upward positive leader initiation at the tip of buildings during the development of downward negative cloud-to-ground flash is discussed. In addition to finding that, the height of the building has a promoting effect on the initiation of the leader. The following conclusions have obtained: 1) for the same IP, the taller the building, the smaller the difference (η) of its geometric on the leader initiation; for the buildings of the same height, as IP increases, the η becomes smaller. 2) The stable leader at the tip of the cylindrical tower type is the easiest to initiate and the closest to the needle, the smallest η have reached at 12.2%. The stable leader at tip of the cuboid type is the latest to initiates, the largest η have reached at 53.4%. 3) For the case of short building and weaker IP, the geometric characteristics of tip (tower or slope) has a significant effect on the leader initiation.