In this paper, we present a linear stability analysis on flow-induced vibration of an elastically mounted cylinder subjected to forced rotation. Four series of cases, with different combinations of degrees of freedoms in oscillation and Reynolds number are investigated. For each series of cases, a wide range of reduced velocity at various rotation rates are considered. The variations of growth and frequency with reduced velocity for the leading modes are presented. Some phenomena observed in previous numerical studies are interpreted by using the results of linear stability analysis. The supressing of vortex shedding at moderate rotation rate is explained by the absence of unstable fluid mode. The amplitude enhancement in high range of rotaton rate is explained by the emergence of unstable elastic mode. The stability properties of the leading modes provide some new insight into the influences of forced rotation on flow-induced vibration. The results of the current study have important implications in the design of offshore structures and energy-harvesting devices.