The present work analyzed the hydromagnetic effect on three-dimensional Couette flow of viscous incompressible, electrically conducting and Newtonian fluid through a porous medium bounded by two horizontal parallel porous flat plates with transverse sinusoidal injection of the fluid at the stationary plate and its corresponding removal by periodic suction through the plate in uniform motion. The flow becomes three dimensional due to this injection/suction velocity. Approximate solutions are obtained for the flow field, the pressure, the skin-friction, the temperature field, and the rate of heat transfer. It is found that the cross velocity w is reduced considerably with a rise in the magnetic body parameter (M), permeability parameter (K) and injection/suction (A) in the forward flow, while a reverse effect is observed in the backward flow. An increase in K or 2 is found to escalate the main flow velocity whereas an increase in the magnetic body parameter (M) is shown to exert the opposite effect. Similarly, the shear stress due to main flow is considerably increased with an increase in M and K. The results show that both methods, perturbation and electrical network schemes provides excellent approximations to the solution of this nonlinear system with high accuracy. The acquired knowledge in our study can be used by designers to control Magnetohydrodynamic (MHD) flow as suitable for a certain application. Other possible applications include materials processing, MHD propulsion thermo-fluid dynamics, boundary layer in aerodynamics, chemical engineering etc. (C) 2016 Elsevier Ltd. All rights reserved.