In order to explore parametrically excitation motions of wave energy converter and its influence on wave energy capture capability, both the frequency domain and time domain simulation models of a multiple degrees of freedom wave energy converter with a vertical axis of symmetry were established based on the potential flow theory. A vertical power take-off (PTO) mechanism was installed inside PTO pipe, allowing a floating buoy to slide along the pipe under wave action. The pitching and rolling articulated shafts are connected with the PTO mechanism respectively, and the corresponding PTO damping torque is proportional to the angular speed of pitching and rolling. Setting damping force of vertical PTO is proportional to the sliding speed of the floating buoy along the PTO pipe, in order to assess the occurrence of large amplitude parametric resonance in the time domain model, when the vertical PTO force is decomposed into vertical and horizontal directions, the nonlinear term is retained, while the nonlinear term was ignored in the frequency domain model. Results show that the parametrically excitation motions are mainly caused by vertical PTO damping force. The wave energy captured by the vertical PTO will be reduced due to occurrence of parametrically excited motions, and a period range of the parametrically excitation motions will become widen with the increase of wave height and vertical PTO damping coefficient. In the following sea waves, both the vertical and pitch PTO were connected with PTO damping, if the damping torque coefficient of pitch PTO is small, then the parametric pitching and rolling occur together. On the contrary, if the pitch PTO damping is large the parametric pitching can be suppressed, but large amplitude parametric rolling will occur. Therefore, in order to completely suppress the parametric resonance of the converter, both pitch and roll PTO mechanisms need to set a certain mount of PTO damping.