In this study, the stabilization of cart-pendulum system with a discrete-time backstepping controller and the attenuation of the disturbance affecting on the cart are considered. In order to enable discrete-time backstepping design discrete-time partial feedback linearization performed and a novel discrete-time coordinate transformation is proposed. Before construction of backstepping controller, a nonlinear disturbance estimator design is proposed with Immersion and Invariance approach in the discrete-time setting. The estimated disturbance values used in the partial feedback linearization and construction of backstepping controller. The performances of proposed algorithms are tested by simulations.