In this study, MHD mixed convection and entropy generation of non-Newtonian power-law fluid inside a partially heated cavity with an adiabatic rotating cylinder under the influence of an inclined magnetic field is numerically studied. The left vertical wall is partially heated and the right vertical wall is cooled while the remaining walls are assumed to be adiabatic. An adiabatic rotating cylinder is located at the center of the cavity. The governing equations are solved by the Galerkin weighted residual finite element method. The effects of the Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), angular rotational velocity of the cylinder (between -50 and 50), inclination angle of the magnetic field (between 0 degrees and 90 degrees) and the power-law index (between 0.6 and 1.4) on the fluid flow and heat transfer characteristics are numerically investigated. It is observed that the averaged heat transfer enhances for the pseudoplastic fluid and deteriorates for the dilatant fluid as the Richardson number increases. Local heat transfer decreases in the lower part of the heater and increases towards the upper part of the heater for Newtonian and shear-thickening fluid with the magnetic field. When the cylinder rotates in the counter-clockwise direction, the averaged heat transfer is deteriorated for the Newtonian and pseudoplastic fluids. The total entropy generation ratio changes for the Newtonian and dilatant fluids with the magnetic inclination angle and cylinder rotational velocity. (C) 2016 Elsevier Ltd. All rights reserved.