In this work, we investigate immiscible displacement in porous media with the displaced fluid being shear-thinning. We focus on the influence the heterogeneous viscosity field in the shear-thinning fluid brings on viscous fingering, which has received little attention in the existing researches. Lattice Boltzmann simulations of immiscible displacement with a power law model implementation in the displaced fluid are conducted. The lattice Boltzmann algorithm is validated against Newtonian and non-Newtonian flows in a channel. The effects of the shear-thinning property and the viscosity heterogeneity on viscous fingering are considered in the simulations. The results show that with stronger shear-thinning property (lower power law exponent n), there is stronger viscosity heterogeneity in the displaced fluid, and the viscous fingering shows weaker instability. The influence of a heterogeneous viscosity field on viscous fingering is dominated by the viscosity in the low-viscosity regions, while the high-viscosity regions show little influence. The influence of the local viscosity on viscous fingering is dependent upon the local shear rate. A concept of effective field viscosity' is introduced to quantitatively characterize a heterogeneous viscosity field. A shear rate weighted averaging algorithm is proposed to calculate the effective field viscosity from a heterogeneous viscosity field. The algorithm is tested in several cases and shows good performance to represent the influence of the heterogeneous viscosity field.