Abstract The viscosity of extra-heavy oils including bitumen can be reduced significantly by adding solvent such as toluene to enhance extraction, production, and transportation. Thus, prediction of viscosity and/or rheology of bitumen-solvent mixtures has become necessary. More so, selecting a suitable rheological model for simulation of flow in porous media has an important role to play in engineering design of production and processing systems. While several mixing rules have been applied to calculate the viscosity of bitumen-solvent mixtures, rheological model to describe the flow characteristics has rarely been published. Thus, in this investigation, rheological behavior of bitumen and bitumen-toluene mixtures (weight fractions of bitumen WB = 0, 0.25, 0.5, 0.6, 0.75, and 1 w/w) have been studied at the flow temperature (75 °C) of the bitumen and in the range of shear rates between 0.001 and 1000 s−1. The data were fitted using different rheological models including the Power law, Cross model, Carreau–Yasuda model, and the newly introduced ones herein named as Cross-Logistic and Logistic models. Then, a computational fluid dynamics (CFD) model was built using a scanning electron microscope (SEM) image of rock sample (representing a realistic porous geometry) to simulate pore scale flow characteristics. The observations revealed that the original bitumen exhibits a Newtonian behavior within the low shear rate region (0.001–10 s−1) and shows a non-Newtonian (pseudoplastic) behavior at the higher shear rate region (100–1000 s−1). Conversely, the bitumen-toluene mixtures show shear thinning (pseudoplastic) behavior at low shear rate region (0.001–0.01), which appears to become less significant within 0.01 to 0.1 s−1, and exhibit shear independent Newtonian behavior within 0.1 and 1000 s−1 shear rates. Moreover, except for the original bitumen, statistical error analysis of prediction ability of the tested rheological models as well as the results from the pore scale flow parameters suggested that the Power law might not be suitable for predicting the flow characteristics of the bitumen–toluene mixtures compared to the other models.