Numerical simulations of a low-mass-damping circular cylinder which can oscillate freely at transverse and stream-wise directions are presented in this work. The Navier-Stokes equations are solved with finite volume method, and large eddy simulation of vortex is also performed in the calculation. In order to implement dynamic mesh, overlapping grids are generated to lessen the computation for mesh field itself. Self-excited vibrations are firstly calculated to obtain the average amplitudes and frequencies of the target circular cylinder in the current flow situation, and then forced oscillations are implemented with parameters obtained in vortex-induced vibrations previously. With slight amplitude modulation, time series of displacements in vortex-induced vibrations are essentially harmonic. Regarding the fluid force, which are larger in forced oscillations than those in corresponding self-excited cases because the fluid subtracts energy from the forced cylinders. The phase angles between forces and displacements are 0° and 180° for self-excited case and forced case respectively. In vortex-induced vibrations, the interactions between fluid and structure produce some weakly energetic vortices which induce the modulations of amplitude and frequency.