Abstract: Bursting oscillation is a fast-slow dynamic phenomenon widely existing in nature. These years， it has been a hot topic on nonlinear dynamics. It usually appears as the transition between large and small oscillations due to bifurcation points or unstable lim it cycles. According to different dynamic mechanisms， bursting oscillation can be divided into various modes such as ‘point-point’mode and ‘point-ring’ mode. This paper focuses on a class of bistable composite laminates of nonlinear systems by parametric excitation and concerns the case where one parameter excitation frequency is an integer multiple of the other. The parameter excitation is regarded as a slow variable parameter， so the fast and slow subsystems of the multi-frequency parameter excitation system are obtained based on the fast-slow analysis method and the bifurcation behavior of the fast subsystem is analyzed. In the bifurcation analysis， the Hopf and fold bifurcation conditions of the fast subsystem with single mode and double mode bifurcation points are investigated. Exploiting double parameter bifurcation sets， phase portraits， time history curves and the overlap of transformed phase portraits with equilibrium branches， the mechanism and dynamic behavior of bursting oscillation with different parameters are studied.It is observed that the bursting oscillation phenomenon with different parameters may be independent of the pitchfork bifurcation points.