A computational fluid dynamics (CFD) modelling approach is used to study the unsteady respiratory airflow dynamics within a human lung. The three-dimensional asymmetric bifurcation model of the central airway based on the morphological data given by Horsfield et al. (J. Appl. Physiol. 67 (1971) 207) was used in the present study to simulate the oscillatory respiratory. The single bifurcation was found to be sufficient to give a number of results which both qualitatively and quantitatively agreed well with other published experimental and CFD results. Numerical simulation were made for two breathing conditions: (a) resting or normal breathing condition and (b) maximal exercise condition. The respiratory flow results for the both conditions are found strongly dependent on the convective effect and the viscous effect with some contribution of the unsteadiness effect. The secondary motions were stronger for the normal breathing condition as compared with the maximal exercise condition. The difference between the two cases is the flow separation regions found close to the carinal ridge for maximal exercise condition. For normal breathing condition no separation regions was observed in this region.