In this article, polypropylene/styrene–ethylene–butylene–styrene grafted with maleic anhydride (PP/SEBS-g-MA) triblock copolymer blends and their samples containing various amounts of organo-modified montmorillonite (1–5 phr) are prepared through melt compounding in an internal mixer. X-Ray diffraction (XRD) and transmission electron microscopy (TEM) are used to evaluate the dispersion of nanoclay particles in the blends. The measurements of mechanical and thermal properties of all the samples are carried out by means of standard methods. XRD and TEM results show existence of exfoliated and intercalated structures in the samples. Furthermore, the measurements of mechanical properties of the samples show that despite the decrease in tensile strength and Young’s modulus of PP in the presence of SEBS-g-MA as a toughening agent, addition of clay as the reinforcing filler improves these properties. So, a good balance between strength/stiffness and toughness/ductility is obtained with the addition of SEBS-g-MA and clay simultaneously and controlling their contents. Finally, thermal studies reveal that addition of clay has no significant influence on the structure and stability of the PP crystals formed.