In the present work, an attempt was made to explore the effect of Polystyrene-b-poly (ethylene-butylene)-b-polystyrene (SEBS) block copolymer morphology on carbon nanotube (CNT) dispersion in SEBS with cylindrical and spherical morphology which were melt mixed with different amounts of CNT. Microstructure of the nanocomposite samples were studied by using both melt linear and nonlinear viscoelastic measurements. The frequency sweep test results showed a pronounced enhancement in storage modulus in low frequency region with greater extent for the SEBS with spherical morphology. This result could be explained in terms of lower viscosity and/or melt elasticity of SEBS with spherical morphology compared to that of cylindrical one. Lower viscosity and/or melt elasticity lead to greater diffusion of polymer chains into nanoparticle agglomerates and better dispersion. The startup flow test results evidenced existence of a 3D network due to block copolymer phase separated microdomains in cylindrical SEBS and its nanocomposites which intensified through addition of CNT.