Based on the four-step semi-implicit Characteristic-Based-Split (CBS) stabilized fluid finite element method, the flow-induced vibration of an elastically supported cylinder with two degrees of freedom in 2D planar shear flow was numerically studied. Besides, the effects of some key parameters, such as natural frequency ratio(r), shear ratio(k) and reduced velocity(ur), on vibration response of the cylinder and fluid field around it were analyzed. The results show that the lock-in range and resonant region of the cylinder broaden as k increases. The reduced velocity has a great impact on the maximum vibration amplitude of the cylinder: the amplitude is larger in the lock-in range; however, it becomes small in  other cases. It is found that, in the resonant region, the orbital trajectory of the cylinder shows an 8-shaped figure at a larger r, whereas it transfers from the 8-shaped figure motion to a raindrop motion with the increase of k at the lower r. The vortex shedding patterns are 2S and P+S in the shear flow.