An adaptive-gain observer is proposed to estimate the state variables of dynamic systems with Lipschitz nonlinearities. Such an observer is derived by the increasing-gain observer, which is a high-gain observer with a time-varying gain that increases over time up to a maximum. As compared with the increasing-gain observer, the proposed estimator allows for the on-line tuning of the gain to compensate for system disturbances that increase the output error. The stability of the estimation error for the adaptive-gain observer is established under suitable conditions. The design of such an observer is accomplished in such a way to reduce the effect of the measurement noise at regime. Simulation results are presented to illustrate the effectiveness of the approach.