Mixed convection flow in a lid-driven cavity in the presence of a uniform partial magnetic field is investigated utilizing the pseudo spectral method based on polyharmonic spline radial basis functions. The two-dimensional problem is concerned in a unit square cavity designed by adiabatic horizontal walls and vertical walls with constant temperatures. The top wall moves either in the positivexor in the negativexdirections. The partial magnetic field is taken into account in the positiveydirection. Working fluid is chosen as air. Efficiency of dimensionless Hartmann number and Richardson number on fluid flow and heat transfer is presented as well as the length and the central location of partial magnetic field. Flow is affected in the direction of vertical partial magnetic field, and is propelled to the other parts of the cavity regarding the central location of magnetic field. In case of middle centered partial magnetic field. The increase in the length of the partial magnetic field and the middle centered partial magnetic field as well reduce the convective heat transfer. The negativexdirected lid-driven cavity has less influence on convection than the positivexdirected lid-driven cavity.