The flow of polymer solution and heavy oil in porous media is critical for polymer flooding in heavy oil reservoirs because it significantly determines the polymer enhanced oil recovery (EOR) and polymer flooding efficiency in heavy oil reservoirs. In this paper, physical experiments and numerical simulations were both applied to investigate the flow of partially hydrolyzed polyacrylamide (HPAM) solution and heavy oil, and their effects on polymer flooding in heavy oil reservoirs. First, physical experiments determined the rheology of the polymer solution and heavy oil and their flow in porous media. Then, a new mathematical model was proposed, and an in-house three-dimensional (3D) two-phase polymer flooding simulator was designed considering the non-Newtonian flow. The designed simulator was validated by comparing its results with those obtained from commercial software and typical polymer flooding experiments. The developed simulator was further applied to investigate the non-Newtonian flow in polymer flooding. The experimental results demonstrated that the flow behavior index of the polymer solution is 0.3655, showing a shear thinning; and heavy oil is a type of Bingham fluid that overcomes a threshold pressure gradient (TPG) to flow in porous media. Furthermore, the validation of the designed simulator was confirmed to possess high accuracy and reliability. According to its simulation results, the decreases of 1.66% and 2.49% in oil recovery are caused by the difference between 0.18 and 1 in the polymer solution flow behavior indexes of the pure polymer flooding (PPF) and typical polymer flooding (TPF), respectively. Moreover, for heavy oil, considering a TPG of 20 times greater than its original value, the oil recoveries of PPF and TPF are reduced by 0.01% and 5.77%, respectively. Furthermore, the combined effect of shear thinning and a threshold pressure gradient results in a greater decrease in oil recovery, with 1.74% and 8.35% for PPF and TPF, respectively. Thus, the non-Newtonian flow has a hugely adverse impact on the performance of polymer flooding in heavy oil reservoirs.