Abstract: The problem of observer design for a class of nonlinear systems is investigated.Using the differential mean value theorem,the nonlinear error dynamics are transformed into equivalent systems.By using the convexity theory and constructing the Lyapunov function,three sufficient conditions are obtained,which guarantee that the estimation error converges asymptotically towards zero.An approach to constructing the observer gain is presented.The proposed approach can be applied in both continuous and discrete time nonlinear systems.Finally,a numerical example is provided to illustrate the effectiveness of the obtained result.