The problem of designing a robust adaptive control for nonlinear systems with uncertain time-varying parameters is addressed. The upper bound of uncertain parameters, considered even in control coefficients, are not required to be known. An adaptive tracking controller is presented and, using the Lyapunov theory, the closed-loop stability and tracking error convergence is shown. In order to improve the performance of the method, a robust mechanism is incorporated into the adaptive controller yielding a robust adaptive algorithm. The proposed controller guarantees the boundedness of all closed-loop signals and robust convergence of tracking error in spite of time-varying parameter uncertainties with unknown bounds. The parametric uncertain systems under consideration describes a wide class of nonlinear circuits and systems. As an application, a novel parametric model is derived for nonlinear Chua's circuit and then, the proposed method is used for its control. The effectiveness of the method is demonstrated by some simulation results.