Cylindrical structures exist widely in nature and engineering. The problem of suppression of vortex-induced vibration of cylindrical structures caused by viscous flow separation has received close attention in past decades. Splitter plate is commonly used as a passive control device due to its effective suppression of vortex shedding, but it is worth of further research about its influence on the VIV of circular cylinder and internal mechanism of VIV suppression. Herein, combining with lift oscillator model and Detached Eddy Simulation turbulence model (DES) and adapting asynchronous iterative algorithm, numerical computation of strong coupling resolved method were carried out by using SIMPLE algorithm and Newmark-\beta method to solve the discrete fluid and structural equations. The accuracy of the strong coupling algorithm based on Detached Eddy Simulation was verified, and then the effect of suppression of splitter plate (L/D=\mathrm{0.5}) on a cylinder with single degree of freedom vibration was studied when the range of reduced velocity was . Moreover, the suppression effect of the splitter plate on the wake mode, responses of fluid force and vibration, and frequency characteristics of vibrating cylinder was analyzed. The critical velocity was obtained. The numerical results show that the vibration can be well suppressed when .The maximum vibration amplitude decreases about 69%, lock-in region of frequency becomes narrow and the vortex shedding frequency decreases obviously. The maximum fluid parameters C_{\mathrm{D},\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}},C_{\mathrm{D},\mathrm{r}\mathrm{m}\mathrm{s}}and C_{\mathrm{L},\mathrm{r}\mathrm{m}\mathrm{s}}, acting on the cylinder, decrease about 40%, 90% and 52% respectively. For cylinder attached a splitter plate, galloping phenomenon occurs as U^{\mathrm{*}}>\mathrm{10}. The vibration amplitude of the cylinder keeps increasing. With the continuous increase of U^{\mathrm{*}}, the separating shear layer reattaches to the splitter plate again, and the cylinder absorbs energy from the flow, which was far greater than the energy consumed by structural damping. The amplitude conti-nues to increase and exceeded that of the smooth cylinder, so the vibration of the cylinder is more severe and vibration of cylinder cannot be suppressed by splitter plate in this region.