The numerical computation of vortex-induced vibration of three circular cylinders in a tandem arrangement with two degrees of freedom has been carried out. The effects of Reynolds number, natural frequency ratio and reduced velocity on the dynamic response and spectral characteristics of three tandem cylinders were analyzed. The results indicate that the Reynolds number and natural frequency ratio have little influence on the amplitude and fluid force coefficient of the upstream cylinder. The frequency locked region of the midstream cylinder increases with the increasing of Reynolds number. The dynamic response of the midstream cylinder is greatly affected by the wake of the upstream cylinder, whereas the effect of natural frequency ratio is small. Meanwhile, when the reduced velocity is small, Reynolds number and natural frequency ratio have great influence on the fluid force coefficient. In addition, the amplitude and the fluid force coefficient of the downstream cylinder are greatly affected by Reynolds number and natural frequency ratio. Reynolds number, natural frequency ratio and reduced velocity have great influence on the main peak amplitude, spectrum component and fluctuation of fluid force coefficients PSD curve. The fluctuation of the PSD curve becomes intense, giving rise to the movement trajectory of cylinder from "8" shape to irregular shape. As natural frequency ratio increases to 2.0, the P+S mode is found in the wake of the upstream cylinder, which leads to the occurrence of asymmetric motion, and the equality of main peaks of the PSD curve of the lift and drag coefficients. Finally, the variation of average power value of excitation load with reduced velocity is similar to that of corresponding structural dynamic response. In the same reduced velocity range, the strength of structural vibration response is directly proportional to the average power value of displacement. When analyzing the power spectral density of lift coefficient in different intervals, the vibration frequency ratio has more influence on the structural vibration response.