A highly viscoelastic worm-like micellar solution is formed in hexa-decyltrimethylammonium bromide (CTAB) in the presence of sodium nitrate (NaNO₃). A gradual increase in micellar length with increasing NaNO₃ was assumed from the rheological measurements where the zero-shear viscosity ($\eta_{0}$) versus NaNO₃ concentration curve exhibits a maximum. However, upon increase in temperature, the viscosity decreases. Changes in the structural parameters of the micelles with addition of NaNO₃ were inferred from small angle neutron scattering measurements (SANS). The intensity of scattered neutrons in the low 𝑞 region was found to increase with increasing NaNO₃ concentration. This suggests an increase in the size of the micelles and/or decrease of intermicellar interaction with increasing salt concentration. Analysis of the SANS data using prolate ellipsoidal structure and Yukawa form of interaction potential between mi-celles indicate that addition of NaNO₃ leads to a decrease in the surface charge of the ellipsoidal micelles which induces micellar growth. Cryo-TEM measurements support the presence of thread-like micelles in CTAB and NaNO₃.