In this work, entropy generation due to laminar viscous incompressible flow of a conducting fluid in the presence of a transverse magnetic field in a porous inclined channel is investigated. Fully developed flow field is solved analytically whereas the solution of the energy equation is obtained by Finite Difference Method (FDM). The boundary conditions at the walls are considered to be constant heat flux. The influence of the applied magnetic field, porous medium and the viscous dissipation on velocity, temperature and entropy generation is examined. The dependence of flow and thermal characteristics on Peclet number (Pe), Brinkman number (Br), Darcy number (Da) and Hartman number (Ha) is analyzed through velocity and temperature distribution as well as Entropy generation number (N-s) and Bejan Number (Be) profiles.