In this paper, we introduce a backstepping control design of a wheeled inverted pendulum. Based on a second-order motion equation of the body angle, an adaptive integral backstepping controller is designed to stabilize the body angle. It is shown that the σ-modification rule in the adaptive update law guarantees the boundedness of the errors in estimating the time-varying signal that is an output of a linear system with every bounded input signal. Then, the stabilizing controller for the wheel angle is constructed by a PD-type positive feedback. The derived controller requires the full-state measurements. In the output feedback case, the K filter or the observer backstepping is needed. However, the structure of the controller becomes complicated. We propose a non-model-based differentiator based on the adaptive update law. Since the non-model-based differentiator does not require any knowledge of the dynamic structure of the signal, we can use it as a velocity estimator for unknown nonlinear systems. Therefore, we replaced the velocity measurement with the estimates by the non-model-based differentiator. Finally, simulation results for the proposed controller are presented.