Chronic obstructive pulmonary disease (COPD) is one of the most common diseases in human community. The COPD always results in inflammation that leads to narrowing and obstruction of the airways. The obstructive airways have significant effect on respiratory flow. In order to understand the flow phenomenon in such obstructive airways, four three-dimensional four-generation lung models based on the 23-generation model of Weibel [1963. Morphometry of the Human Lung. Springer, Academic Press, Berlin, New York] are generated. The fully three-dimensional incompressible laminar Navier-Stokes equations are solved using computational fluid dynamics (CFD) solver on unstructured tetrahedral meshes. Therein, a symmetric four-generation airway model is served as the reference, the other three models are considered to be obstructed at each generation, respectively. The calculation results show that the obstructive airway has significant influence on the air flow in both up- and down-stream airways and it even results in flow separation in the conjunction region. The re-circulation cell blocks the air from entering the downstream branches. This may be the reason why COPD patients should breathe gently, and this also provides some valuable information for medicine powder deposition.