Abstract: This paper studies the normalized kurtosis and its application in blind identification of weak nonlinear system. First of all, some commonly used nonlinear models with or without memory are briefly introduced; then this paper presents the definition of normalized kurtosis and its some useful properties in system identification; according to the definition and properties, the influences of memory depth and nonlinear order on normalized kurtosis are derived theoretically, and simulation result demonstrates the rule of normalized kurtosis varying with the change of system characteristics. This shows that normalized kurtosis has the ability to identify weak nonlinear system accurately. Accordingly, this paper proposes a step by step method to blindly identify extremely weak nonlinear system whose SFDR(Spurs Free Dynamic Range) is up to 85dBFS(dB Full Scale) by using normalized kurtosis. Finally, combined with the proposed method, this paper analyzes the potential value and accuracy advantage in blindly identifying and compensating the weak nonlinear system.