Based on the basic theory of chaos dynamics,Lyapunov exponential index number of the difference equation,controlling the dynamical characteristics of Non-linear Fabry-Perot(NFP) resonator,has been calculated. Using the relationship between Lyapunov exponential index number and NFP, the dynamical characteristics of NFP have been studied. The parameter region of the NFP outputs stable intensity, and the mechanism of conversion from stable state to chaos, have been analyzed and made out.