A numerical study of laminar magnetohydrodynamic mixed convection in an inclined lid-driven squarecavity with opposing temperature gradients is presented. The vertical sidewalls are assumed to havenon-uniform temperature variation while the top and bottom walls are kept insulated with the topsurface moving at a constant speed. The transport equations are given in terms of the stream functions-vorticity formulation and are non-dimensionalized and then solved numerically by an accurate finite-volume method. The computation is carried out for wide ranges of the inclination angle (0 ≤  ≤ /2), theRichardson number (0.01 ≤ Ri ≤ 100), the Hartmann number (0 ≤ Ha ≤ 100), the amplitude ratio (0 ≤ ε ≤ 1)and the phase deviation (0 ≤  ≤ ). The results indicate that the rate of heat transfer along the heatedwalls is enhanced on increasing either Hartmann number or inclination angle. Average Nusselt numberis also, increased with increasing of the amplitude ratio for all values of the phase deviation. The non-uniform heating on both walls provides higher heat transfer rate than non-uniform heating of one wall.