This paper presents the numerical solutions of a two-dimensional laminar flow over a backward-facing step in the presence of the Lorentz body force. The Navier-Stokes equations in a vorticity-stream function formulation are numerically solved using a uniform grid mesh of $2001{ imes}51$ points. A second-order central difference approximation is used for spatial derivatives. The solutions progress in time with a fourth-order Runge-Kutta method. The unsteady backward-facing step flow solution is computed for Reynolds numbers 100 to 800. The size and genesis of the recirculating regions are dramatically affected by applying the Lorentz force. The results demonstrate that using an appropriate configuration for applying the Lorentz force can make it an essential tool for controlling the flow in channels with a backward-facing step.