We investigate bias and different barrier thicknesses effects on quantities related to spin and charge currents in MgO-based magnetic tunnel junctions. Using the non-Equilibrium Green’s function formalism, we demonstrate that the in-plane and out-of-plane components of the spin-transfer torque have asymmetric and symmetric behaviors respectively. Magneto-resistance also decreases with increasing barrier thickness. The Landau–Lifshits–Gilbert equation describes the dynamics of the magnetization made by spin transfer torque. Increasing in spin current above its critical value or smaller the magnet reduces the switching time which is major result for making of new memory devices.