This paper presents numerical simulation results for vortex-induced vibration of a circular cylinder in laminar flow. A vortex method is implemented to solve the two-dimensional Navier-Stokes equations in terms of vorticity. In order to validate the numerical code, the flow past a fixed cylinder is first investigated for which enough experimental and numerical results are available. Basic characteristics of the dynamic response and vortex shedding for an elastically mounted circular cylinder are then investigated for 70 < Re < 170. The lock-in phenomenon is captured at certain reduced velocities where the lift coefficient takes a considerable value associated with a high amplitude response. The wake structure exhibits the 2S or C (2S) modes of vortex shedding in this range of Reynolds numbers, as opposed to the 2P mode which is observed in the turbulent flow regime. The numerical results are in acceptable agreement with available experimental and numerical data.