The effort of reducing the carbone dioxide emission, the problems for fossil fuel and nuclear, a number of investigation to new and renewable energy is dramatically increasing. One of them, The wind power generation systems currently installed on seas are divided into fixed and floating structures according to their support structures. Among various type of floater, the cylindrical structure has a very long period of heave and pitch motion response on the ocean waves. To get the dynamic stability of the cylinder structure, it is required to obtain suitable metacentric height (GM). However, the structure has sufficient metacentric height, when the natural frequency of heave motion is doubled with the natural frequency of roll and pitch motion, the Mathieu instability can be arisen. This paper carried out numerical calculation and experiment regarding vertical axis wind turbine with cylindrical floater which has three different center of gravity. In the regular wave experiment, divergence of the structure motion without Yaw is observed when natural frequency of the heave motion is doubled with the natural frequency of roll and pitch motion. Upon the result of tension response in regular wave experiment with catenary mooring system, the mooring lines in the front of the structure have a bigger tension effect to the offset of the structure than the mooring lines at the back of the structure. In the irregular wave experiment, the motion spectra of structure motion are compared with each different center of gravity and one of the motion spectra of structure is very high when the natural frequency of heave motion is doubled with the natural frequency of roll and pitch motion. The dynamic response spectrum of the structure in the irregular wave experiments showed no significant differences in response following difference of mooring system. As a result of the comparison of the tension response spectrum, the mooring lines have a greater value for heave motion, as shown in the previous regular wave experiment. The results of the dynamic response of the structure in irregular wave and wind, Heave motion response is influenced by the couple effect with the mooring lines by the surge and pitch motion. Also offset of the structure due to the wind, the mooring lines in front of the structure have a very large tension force compared to the mooring lines in front of the structure.