Abstract: Vortex-induced vibrations (VIVs) of slender cylindrical structures in cross flow are ubiquitous in engineering applications. In previous studies, VIVs of a circular cylinder in cross-flow and/or streamwise directions have been well investigated, while little work has been done on the angular response. In this paper, VIV features of an eccentrically rotating circular cylinder in laminar flow is studied numerically. Firstly, the mechanics model of VIV of an eccentrically rotating cylinder is established, and the corresponding governing equations and boundary conditions are derived. Subsequently, coupling the characteristic-based split finite element method, dual-time step method, segment spring analogy technique, generalized-α method and loosely-coupled partitioned method, a fluid-structure interaction (FSI) solution procedure for rotational response of a solid body in laminar flow is developed, and its stability and accuracy are examined by using a benchmark vortex-induced rotation model. Finally, using FSI simulation, effects of eccentricity, Reynolds number and mass ratio on VIV amplitude, frequency and fluid loads of the eccentrically rotating cylinder are investigated in details.