A numerical study is presented for mixed convection flow of air (Pr=0.71) within a parallel motion two sided lid-driven parallelogrammic cavity in the presence of magnetic field. The left and right lid-driven sidewalls of the parallelogrammic cavity are maintained at isothermal hot and cold temperatures respectively and slide from bottom to top in upward parallel direction with a uniform lid-driven velocity. A magnetic field of strength (Box) is subjected in the horizontal direction. The horizontal walls of the cavity are considered thermally insulated. The finite volume method has been used to solve the governing Navier–Stokes and energy conservation equations of the fluid medium in the parallelogrammic cavity in order to investigate the effect of magnetic field on the flow and heat transfer for various values of Richardson number, skew angle and Hartmann number. The values of the governing parameters are the Hartmann number (0 ≤ Ha ≤ 75), Richardson number (0.01≤ Ri ≤100) and skew angle (-60° ≤ Φ ≤60°). The present numerical approach is found to be consistent and the results is presented in terms of streamlines and isotherm contours in addition with the average Nusselt number. It is found that as the Hartmann number increases the circulation of the rotating vortices is reduced and the conduction mode of heat transfer is dominant. Also, it is found that both Richardson number and direction of two sided lid-driven sidewalls affect the heat transfer and fluid flow in the parallelogrammic cavity.