A second-order accurate lattice Boltzmann model is presented for non- Newtonian flow. The non-Newtonian nature of the flow is implemented using a power law model. This is used to enable the accuracy of the model to be assessed and is not a limitation of the model. The second-order accuracy is demonstrated for a range of power law model parameter values representing shear thinning and shear thickening fluids. These results are compared with those of Gabbanelli et al (2006 Phys. Rev. E 72 046312) and it is noted that a higher order of accuracy and greater computational efficiency are achieved. These results demonstrate the suitability of the LBM for shear-dependent non- Newtonian flow simulations.