One of the measures of suppressing vortex-induced vibration (VIV) for the offshore riser is to install a streamlined fairing device. However, the galloping phenomenon may occur for a non-rotating water-drop fairing, which has a serious influence on the riser operation. An improved meshless discrete vortex method (DVM) in a two-dimensional framework is employed to calculate the fluid forces for flow past an arbitrary geometry. Meanwhile, by coupling the mass-damping-stiffness kinematic equation, VIV responses of a circular cylinder with one degree-of-freedom (DOF) under a wide range of reduced velocities can be determined. Then, systematic simulations are carried out to investigate the effects of physical parameters, including free-stream velocity and trailing edge angle, on the galloping characteristics of fairing structures. At last, a quasi-three-dimensional DVM-finite element method (FEM) coupled strategy is employed to calculate the vibration responses of a flexible riser attached with the water-drop fairing. The results indicate that the non-rotating water-drop fairing can bring about intense galloping instability behaviour. The predicted vibration amplitudes, frequencies and fluid forces for different fairings as well as the circular cylinder are compared. Furthermore, a comparison between flow-induced vibration (FIV) characteristics of the bare riser and flexible risers fitted with various fairing devices is conducted.