The synchronizing problem of a chaotic system is investigated based on the observer design. The nonlinear section is assumed to satisfy the Lipschitz condition. Firstly, the normal observer is designed based on the known Lipschitzconstant and the results are given in linear matrix inequality (LMI) form. Then a fairly simple adaptive observer is designed with the Lipschitz constant unknown. Simulations on synchronizing the Lorenz system are investigated and the results show the validity and feasibility of our main results.