Flows of wormlike micellar solutions in an axisymmetric capillary channel were studied both numerically and experimentally. In the experiments, an aqueous solution of cetyltrimethylammonium bromide (CTAB) with sodium salicylate (NaSal) was used as a test fluid. The mole concentration of CTAB is 0.03 mol/l, and that of NaSal is 0.06 mol/l. The velocity distribution was measured with a particle tracking velocimetry and flow visualization experiments were performed. The velocity profile showed a plug-like shape and had inflection points where the velocity gradient rapidly changed. High-shear-rate regions near the channel wall spread with increasing the average velocity. Moreover, the flow turned out to be unstable at high average velocities, and when the flow was unstable, white turbidity was observed near the capillary wall. Shear rates showing a white turbidity were included in the range of shear rate where a shear-rate jump in a flow curve occurred. These results suggest that both the characteristic velocity profile and the emergence of white turbidity relate the shear-rate-jump property of wormlike micellar solution. In the numerical analysis, startup flows were considered. A modified Bautista-Manero model was employed as a constitutive equation, and startup flows at a constant average velocity were numerically simulated. The velocity profile at steady state predicted by the numerical simulation adequately agreed with corresponding experimental data. The velocity profile changes from Newton-like to plug-like with time. Inflection points in velocity profile appeared and moved towards the center-side with time. Temporal changes in both velocity gradient and fluidity indicated that the behavior in velocity depended on the shear-rate-jump property of wormlike micellar solution. The velocity gradient rapidly changed around the inflection point and the range of velocity gradient corresponds to that where a white turbidity was observed in the experiments.