This study presents a nonlinear observer that estimates structured and unstructured uncertainties based on a control methodology that is an adaptive backstepping sliding mode controller to aim wheel slip tracking of a car-like robot. In the vehicle system, the scaling factor for the lengthwise force between tire and road contact is considered as unknown, then adaptation law with Lyapunov-based analysis is derived for the unknown parameter. The lump uncertainties estimated values that are estimated by the nonlinear disturbance observer and the scaling factor estimated values are directly applied in the control input. The closed-loop system stability under the proposed controller is proven using Lyapunov's stability analysis. Then, the adaptive backstepping sliding mode controller's performance with the nonlinear disturbance observer is verified through simulations by comparing to the neural network (radial basis function) observer, which is estimated as the lump uncertainties on quarter-vehicle dynamics.