The present work proposes for the first time a mathematical model for describing the rheological behavior of heavy and extra-heavy crude oils in the presence of nanoparticles. This model results from the combination of two existing mathematical models. The first one applies to the rheology of pseudoplastic substances, i.e., the Herschel-Bulkley model. The second one was previously developed by our research group to model the rheology of suspensions, namely the modified Pal and Rhodes model. The proposed model is applied to heavy and extra heavy crude oils in the presence of nanoparticles, considering the effects of nanoparticles concentration and surface chemical nature, temperature, and crude oil type. All the experimental data evaluated exhibited compelling goodness of fitting, and the physical parameters in the model follow correlate well with variations in viscosity. The new model is dependent of share rate and opens new possibilities for phenomenologically understanding viscosity reduction in heavy crude by adding solid nanoparticles and favoring the scale-up in enhanced oil recovery (EOR) and/or improved oil recovery (IOR) process.