The rheological behavior of polymer nanocomposites plays a significant role in industrial processing. Understanding this behavior is crucial to conducting important commercial processes such as extrusion and injection molding. The ability to predict rheological behavior using constitutive modeling is of significant scientific and practical interests. However, research on constitutive modeling of polymer nanocomposites is scarce. The present study describes experimental and simulation results of the rheological behavior of multi-walled carbon nanotube (MWCNT)-filled polypropylene (PP) nanocomposites with different filler loadings. Rheological behavior was characterized in small amplitude oscillatory shear (SAOS) flow, large amplitude oscillatory shear (LAOS) flow, startup of shear flow, steady shear flow, and stress relaxation after the imposition of a step shear strain. Virgin PP and PP with CNT loadings of 1, 3, and 5 wt% were used. The formation of a rheological percolation network observed at these loadings. The Leonov model, that assumes dominant effect of particle-particle interactions, and Simhambhatla-Leonov model, that assumes polymer-filler interactions dominate over filler-filler interactions, used to simulate the rheological behavior. Model parameters for matrix and nanofiller modes, obtained from SAOS and step-shear experiments at small strains, used to predict nonlinear rheological behavior. In the linear region, the simulations provided good predictions of the experimental data for both the unfilled and filled PP. In the nonlinear region, the simulations also provided good results for the virgin PP and satisfactory results for the PP/1wt%CNT nanocomposite under most flow conditions. However, for the other two composites the model only showed limited success.