Vortex-induced vibrations (VIV) of two elastically mounted circular cylinders with different diameters in tandem arrangement are investigated in a two-dimensional (2D) numerical simulation. The fluid domain is simulated by solving 2D Reynold-Averaged Navier-Stokes equations. Meanwhile, the VIV response of the structures is obtained by solving the motion equation using the 4th Runge-Kutta method. The parameters of the cylinders are designed according to an experimental study of flexible risers. Simulation of an elastically mounted single cylinder is firstly carried out and compared with published experimental results to verify the method utilized in the paper. The results of single cylinder show the response frequencies of the bluff cylinders and the flexible cylinder are comparable. In the simulation of the tandem cylinders, a “frequency capture” phenomenon that the oscillation frequencies of downstream cylinder are locked on to that of the up-stream one although they are with different diameters is observed. It also occurs in the experimental study of flexible cylinders. The mechanism behind is analyzed in the paper.