Intuitionistic observations of phase and Melnikov have defaults in the judgment of system states in the weak signal detection based on the Doffing chaos oscillator. In order to improve the accuracy of the judgment of the system states reliability of signal detection, this paper proposed the method that use Lyapunov exponent to quantitatively judge and to analyze the states of the detection system. The Lyapunov exponent spectrum of the Doffing system was computed on the basis of states of the system judging by Lya- punov exponent; the author also analyzed the relationship among the amplitude of the inner drive signal, Lyapunov exponent and the system states. The results showed that Lyapunov exponent can quantitat ively and accurately judge the states of the detedion system.