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In this paper, we have investigated an unsteady, magnetohydrodynamic convection flow of a double-diffusive viscoelastic fluid past an inclined permeable plate in the presence of viscous dissipation and heat absorption. A transverse magnetic field of uniform strengths is applied perpendicular to the plate along the direction of the flow. The nondimensional governing equations have been solved by using a multiple perturbation method, subject to the corresponding boundary conditions. The effects of various physical parameters on flow quantities such as velocity, temperature, and concentration are studied through graphs. The expressions for local skin friction, Nusselt number, and Sherwood number are derived and discussed with the help of tables.