Shear-induced thickening/thinning phenomena of aqueous rodlike micellar solutions of cetyltrimethylammonium bromide (CTAB) and sodium p-toluene sulfonate (NapTS) were investigated by means of simultaneous measurements of rheology and small-angle neutron scattering (SANS), the so-called Rheo-SANS. The aqueous CTAB/NapTS solutions were classified into five different categories dependent on their flow behavior and micellar structure. By increasing salt concentration and/or shear rates, the micelles underwent morphological transition from (i) spherical or short rodlike micelles to (ii) long rodlike micelles without entanglements, followed by (iii) those with entanglements. These transitions were recognized as changes in flow behavior from Newtonian to shear-thickening and shear-thinning flow, respectively. In the latter two cases, anisotropic SANS patterns appeared around these critical shear rates. The physical meaning of the anisotropic SANS patterns accompanied by shear-thickening flow behavior is discussed in conjunction with other shear-thickening systems.