The concentration of neutrophils in the pulmonary microvasculature is higher than in systemic large vessels. It is thought that this high concentration of neutrophils facilitates their effective recruitment to sites of inflammation. Thus, it is important to clarify the flow characteristics of neutrophils in the pulmonary microvasculature to understand their functions and behavior in the immune system in lungs. For that purpose, authors investigated the flow characteristics of single neutrophil in a capillary segment to develop a mathematical model to predict the transit time of the cell through the segment. This model was then extended for application to simulate the flow of neutrophils in a capillary network, and we investigated the effect of cell stiffness on the transit time of the cells through a simple lattice capillary network. In this study, similar lattice network was introduced and the effect of geometry of capillary segments on the transit time of neutrophils through the network was investigated. Finally, it was shown that average transit time of the cells through the network and the coefficient of variation increase as the capillary segments become steep or tight. Relationship between the rise in the concentration of the cells and segment geometry was also presented.