The viscous fingering instability of miscible displacements in the presence of permeability heterogeneity is studied. Shear-thinning fluids are successful to suppress this instability where the mobility ratio is high and/or the heterogeneity of the porous medium is adverse. The displacing fluid is considered a non-Newtonian fluid, and the shear-thinning characters of it have been modeled using the Carreau-Yasuda constitutive equation. Two different heterogeneity models are used in this simulation, one in which the permeability decreases in transverse direction exponentially and the other in which the permeability decreases and increases exponentially in longitudinal direction, separately. In particular, the role of permeability heterogeneities on the differences between Newtonian and non-Newtonian fluids is investigated through linear stability analysis and nonlinear simulation. In nonlinear simulations, using a spectral method based on the Hartley transforms, nonlinear finger interactions, mixing lengths, sweep efficiencies, and transversely average concentration are examined and compared in Newtonian and non-Newtonian displacements.