For the purpose to estimate the state of nonlinear continuous-time systems, we focus on the increasing-gain observer regarded as generalization of the well-known high-gain observer. As compared with the previous results on increasing-gain observers, the assumptions under which the global asymptotic stability of the estimation error is proved are relaxed. The stability analysis is drawn by using a more general type of Lyapunov functional, where design parameters can be tuned to set the time-varying gain. A new design method based on such a Lyapunov functional is proposed to construct the observer. Simulation results affirm the effectiveness of the increasing-gain approach as compared with the high-gain observer. (C) 2015 Elsevier Ltd. All rights reserved.