Abstract: Considering that the characteristic of Logistic chaos system varies in the relationship of the parameter, and the feature of that the relative entropy reflects the lack of equilibrium, this paper proposes a new method to estimate the characteristic of Logistic chaos system based on symbolic relative entropy. Numerical simulations prove that, Logistic chaos system possesses the property of time irreversibility which increases with parameter and is irrelevant with initial value x0. Accordingly, a novel quantifiable nonlinear dynamical behavior index is obtained, which provides the theoretical basis for understanding Logistic chaos characteristic and chaos control.