Abstract In this paper, the flow-induced vibrations of an elastically mounted circular cylinder subjected to the planar shear flow with the 1-DOF (only transverse direction) and 2-DOF (in-line and cross-flow directions) movements are studied numerically in the laminar flow (Re=150). Based on a characteristic-based-split (CBS) finite element method, the numerical simulation is conducted, and is verified through the benchmark problem of the uniform flow past an elastically mounted circular cylinder. The computation is carried out for lower reduced mass of Mr=2.0 and the structural damping ratio is set to zero to maximize the vortex-induced response of the cylinder. The effects of some key parameters, such as shear rate (k=0.0–0.1), reduced velocity (Ur=3.0–12.0) and natural frequency ratio (r=1.0–2.0), on the characteristics of vortex-induced vibration (VIV) responses are studied. The results show that, in the 1-DOF system, the frequency synchronization region extends with the increasing of k. The shear rate greatly affects the phase portraits, which shift from the double-valued type to the single-valued one. On the other hand, in the 2-DOF system, the increasing of k causes the extension of the single-resonant region and dual-resonant one at the lower natural frequency ratios. While at the higher natural frequency ratios, the change of k only expands the single-resonant region in the transverse direction. The predominant vortex shedding patterns are 2S and P+S modes. Finally, the interaction between vortex and cylinder as well as the mechanism of flow-induced vibration in planar shear flow are revealed. The phase between the force and its corresponding displacement changes from out-of-phase to in-phase and the higher harmonic forces appear with the increasing of shear rate, resulting in the energy transferring from the fluid to the structure and then the dynamic response of the cylinder intensifying.