Abstract The structures of flow in laminar Couette-Taylor flow with periodic oscillation of the inner cylinder rotation velocity (which linearly increases from zero to a fixed maximum value and then goes to zero again in each period) for different three regimes; Couette flow, Taylor vortex and wavy vortex, with the effect of the Womersley number, Wo, for different periods and the critical Taylor number are investigated numerically. The Wo varies between. 0.38 ≤ Wo ≤ 8.59. To understand how the flow responds to a given boundary conditions, the critical Taylor number is calculated and the structure of vortices which formed in the flow field is investigated. The results show that if Wo is increased, i.e. when the slope of rotational velocity of inner cylinder is increased, more delay in changing the flow regime compare to the steady state (when the inner cylinder rotates with constant velocity) is observed. Also for large values of Wo, due to the inertia, the flow does not follow the given boundary condition so for the higher value of the Womersley number, Wo = 8.59, there is a time lag and vortices do not appear until the second period of the inner cylinder oscillations. The reason is that the time scale of the dynamics of flow is less than the time scale that is associated with the flow instability, thus the flow regime behaves like a laminar Couette flow at the initial period. Comparing the present results with that of steady state, it is appeared that for a minimum value of Wo used in this paper, i.e. Wo = 0.38, the primary critical Taylor number is 50% higher than that of steady state.