The riser will be subject to platform heave forces during operation, which causes the axial force to change periodically, causing parametric vibration.Therefore, it is instructive to study the parametric vibration of the riser to avoid parametric resonance.This paper considers the force of the drilling fluid on the riser and establishes the transverse vibration control equation of riser by using the micro-element method.Assuming that the axial force changes periodically, the Mathieu equation of the riser is obtained. And the parametrically excitedvibration stability analysis of the riser is performed based on the Floquet theory.The results showed that the main instability zone occurred near one-half of the natural frequency of the riser.With further study for the influence of damping on the system parameter stability, it is found that the damping increases the stability area of the riser, and the larger the damping, the greater the stable area is.The research of this paper provides reference for avoiding theparametricallyexcited resonance in the design of the riser.