The structure of a cationic worm-like micelle at two concentrations, dilute and semi-dilute in aqueous solution, was studied by a combination of small-angle neutron scattering (SANS) and light scattering. It is found that the shape of the micelles can be best described as a rod with a large aspect ratio. SANS data were determined for the systems under shear. For the semi-dilute solution, we observed that the scattering pattern became anisotropic, as expected. Anisotropy was observed in the dilute solution, but only after a threshold shear rate was exceeded. Details of the anisotropic patterns, moreover, depended on the micelle concentration.