Abstract.A numerical study is conducted to understand the effect of magnetic field on the natural convection in a tilted parallelogrammic porous enclosure. The two opposing side walls are differentially heated with a temperature difference specified, while the upper and lower walls are adiabatic. Using the Darcy model to formulate the problem, a finite difference scheme consisting of the Alternating Direction Implicit and Successive Line over Relaxation methods are used to solve the coupled non-linear governing equations. Computations are carried out for a wide range of Rayleigh number ranging from 100 to 5 × 10 3 , inclination of the walls of the parallelogram ϕ from -60 0 to 60 0 , angle of inclination of the enclosure α from -60 0 to 60 0 , aspect ratio from 0.5 to 2 and Hartmann number from 0 to 20. The flow structure and the corresponding heat transfer characteristics inside the enclosure are presented in detail. The results revealed that both the magnetic force and the inclination angle have significant effect on the flow field and heat transfer in porous medium. The reported results are in good agreement with the available published work in the literature.