This paper presents an adaptive robust controller for a class of uncertain chaotic Rossler system with time-varying mismatched parameters. The proposed controller is designed based on Lyapunov stability theory, and it is shown that using this controller all signals of the closed-loop system are uniformly ultimately bounded (UUB). In addition, the proposed scheme is such that it does not require a priori information about the bound of uncertainties. Furthermore, since all the signals are UUB, the control signal is smooth and feasible to implement. Simulation results on a third-order Rossler system with time-varying parameters confirm the effectiveness of the proposed controller.