This paper numerically investigates the flow-induced vibration of a circular cylinder attached with front and/or rear splitter plates at a low Reynolds number of Re = 120. The effects of plate length and plate location on the hydrodynamic coefficient, vibration response, and flow wake are examined and discussed in detail. The results reveal that the hydrodynamic coefficient of the cylinder with a single rear plate is significantly reduced at Ur ≤ 8 (Ur is the reduced velocity), resulting in the vortex-induced vibration (VIV) suppression. Nevertheless, the galloping is excited at Ur > 8 due to the hydrodynamic instability, accompanied by the jump of response amplitude and hydrodynamic force, as well as the abrupt drop of response frequency. The alternate reattachment of shear layers on the plate surface introduces an extra lift force that strengthens the vibration response. By introducing an individual front plate, significant VIV suppression is achieved. The vibration exhibits variable patterns when the cylinder is equipped with bilateral plates, including the typical VIV mode, weak VIV-galloping coupling mode, and IB-galloping-DB mode (IB and DB represent the initial branch and desynchronization branch of VIV, respectively). The galloping branch in IB-galloping-DB mode is observed with an abrupt drop in response frequency, as well as a tiny time lag between the displacement and lift force. The vibration response is significantly suppressed when the cylinder is simultaneously equipped with a 1D front plate and a 1–2D rear plate due to the streamlined profile.