Intermittent vibration refers to the state in which the laminar flow in fluid is interrupted by turbulent outbreaks at irregular intervals. In the field of nonlinear dynamics, the intermittent motions is termed the pseudo random alternating motion between regular motion and irregular motion. Intermittency is a typical route to chaotic motions for nonlinear dynamical systems. However, for the behaviors of intermittency chaos, the research methods have yet to be enriched due to the parametric sensitivity and evolution complexity of the nonlinear dynamic responses. The semi-analytical and seminumerical harmonic balance and alternating frequency/time domain (HB-AFT) method can avoid the traditional integral or series expansion of complicated nonlinear terms, which make it obtain a harmonic solution of the system quickly and accurately. Based on the HB-AFT method and Floquet stability theory, this paper presented a new semi-analytical method for the evolution of intermittency chaos in nonlinear dynamical systems. Taking the classical singlefrequency excitation Duffing system as an example, the global periodic solution branches and their instabilities are analyzed, and the dynamic evolution mechanism of a type I intermittency chaos is illustrated.