Startup flows of wormlike micellar solutions in an axisymmetric capillary channel were numerically studied using a modified Bautista-Manero (MBM) model as a constitutive equation. The values of model parameter of the MBM model decided for a CTAB/NaSal solution were employed. The velocity profile at steady state predicted by the numerical simulation agreed with corresponding experimental data. The present study treated startup flows at a constant pressure gradient, which corresponds to a stress-controlled-type flow. The flow rate increased with time until the flow reached a steady state. The velocity profile had an inflection point around which the velocity gradient rapidly changed. The position of inflection point slightly changed with time. Temporal changes in both fluidity and the micellar contribution to shear stress occurred within a wall side region of the inflection point, where a white turbidity phenomenon was observed in our previous experiments. These temporal responses are characteristic of the startup flow at constant pressure gradients.