To the synchronization problem of the chaotic systems with uncertainties and not all the state variables are measured,a nonlinear observer is designed based on Linear Matrix Inequality (LMI) method.Assuming that the nonlinear variable satisfies a certain condition,the designed controller will synchronize with the drive system.The existence of the controller is given in terms of a LMI,and the design of the controller is obtained by solving the LMI.Moreover,a secure communication scheme is given by using the observer designed.Finally,analysis of the synchronization system and numerical simulation are presented to show that the method proposed is effective.