Abstract: In order to master the vortex-induced vibration laws of marine riser system, the generalized α method was developed to solve the cylinder vibration equation, and the stability of the solution method was enhanced. After the flow field equation was solved by the improved Characteristic Based Split (CBS), a fluid-solid coupling finite element method was developed to calculate the problem of vortex-induced vibration. In addition, the accuracy and stability of the solution method were verified using a benchmark example. Finally, this solution method was applied to numerically simulate the vortex-induced vibration process of two staggered circular cylinders under various working conditions at low Reynolds number. The results show that when the attack angle is small, the vortex shedding from the upstream cylinder interacts directly with the downstream cylinder, which increases the pressure difference between the upper and lower surfaces of the downstream cylinder, resulting in large-scale vortex-induced vibration. And at this moment, the vibrating frequency of the downstream cylinder is dominated by the shedding process of the vortex from the upstream cylinder. When the attack angle is large, the downstream cylinder will be separated from the wake region of the upstream cylinder, and its flow field, force and vibrating frequency are close to the case of single cylinder. The research results can provide some reference for the layout of marine riser system in engineering practice.