In this paper a systematic observer-based multiple-model adaptive controller design method is proposed for Lipschitz nonlinear systems. By introducing a compensator in the observer-based controller, the uncertainty due to the estimation error is decreased and the steady-state response is improved significantly. In order to deal with the uncertainty of system dynamics, a multiple-model switching scheme is introduced to improve the transient performance. A state-dependent dwell-time-based switching logic is used to ensure the asymptotic stability as it can cancel the possible increase of Lyapunov function in each switching. A simulation result is given to demonstrate the effectiveness of the proposed method.