Abstract: Based on the interpolation-supplemented lattice Boltzmann method and constitutive equation for power-law fluid, a lattice Boltzmann model for power-law fluid in body-fitted coordinates is proposed and applied to simulate steady and unsteady flows of a power-law fluid past a circular cylinder, respectively. The non-equilibrium extrapolation boundary scheme is adopted for the non-slip velocity at the circular cylinder surface. The drag coefficient and lift coefficient are calculated by integrating the total stresses on the boundary of the circular cylinder, respectively, and the results are in good agreement with those obtained by using the conventional lattice Boltzmann method and finite volume method. After performing the grid sensitivity tests, in terms of steady flow, the effects of power-law index on the wake length, separation angle, viscosity distribution over cylinder surface, pressure coefficient and drag coefficient are further analyzed. Moreover, as for unsteady flow, the influences of power-law index on the flow field, drag coefficient, lift coefficient and Strouhal number are investigated. The validation and capability of the model are demonstrated by the good agreement between the simulation results and the ones obtained by other numerical simulation methods. The simulations show that the interpolation-supplemented lattice Boltzmann method can be used to study power-law fluid flow in flow field with complex boundaries, and it can be further applied to study other types of non-Newtonian fluid flow problems by using different constitutive equations.