We study tunnel barrier thickness effects on spintransfer torque (STT) components, charge current, and thermal-shot noise power in an MgO-based magnetic tunnel junction (MTJ) nanostructure using non-equilibrium Green’s function (NEGF) formalism. Also, the bias dependence of the in-plane and perpendicular torkances is investigated. From the NEGF calculations, we find that the STT components are independent of barrier thickness. Magnetization dynamics is described by the Landau-Lifshits-Gilbert (LLG) equation. The charge current decreases for increasing barrier thicknesses. The thermal-shot noise shows linear behavior with increasing of bias voltage for different barrier thicknesses.