The power take-off (PTO) damping mechanism is very important to the motion and power conversion for the wave energy converters. Based upon the potential flow theory, the series expression with unknown Fourier coefficients of velocity potential function of the basin where the cylindrical floating buoy is located is obtained by using the eigenfunction expansion method. According to the characteristics of the PTO damper, the motion and wave energy conversion characteristics of the float under the linear and non-linear PTO damping are studied, respectively, and the over-damping problem under the linear PTO damping is emphatically explored. The results show that the influence of PTO system with low velocity index on the motion of the device is mainly reflected in the PTO damping coefficient. With the increase of damping coefficient, the resonance frequency of the wave energy device decreases gradually, but the decrease amplitude is very small. The non-linear characteristics of PTO system cannot change the optimal capture width ratio of the float, but the large velocity index can effectively improve the damping capacity of PTO system. At lower and higher frequencies, the optimal PTO damping obtained by the analytic algorithm will make the device in an over-damped state. The highest frequency in the low frequency part and the lowest frequency in the high frequency part which need to be modified will gradually decrease with the increase of radius and draught.