Although slamming vibration and significantly nonlinear wave-induced vibration have not occurred, in thevibration response of the hull induced by low-frequency wave load, there still exists high-frequency vibration components, which decay slowly. Based on single-degree of freedom system harmonic excitation vibration theory, paper points out the associated free vibration which item is often overlooked in the response analytical solution is one factor of high-frequency vibration factors, transient response component is difficult to decay when system damping is small and natural frequency is low,accounting laws are derived on high-frequency components of internal force response of displacement, velocity, acceleration and force. The characteristic of wave loads are "time-changing and field-changing" when act on ships is analyzed, reputing associated free vibration play an important role in the prediction field of vibration response excited by wave load, compared theoretical differences of time domain and frequency domain method, discovered the advantages of time-domain method in dealing with this issue.Vibration responses under 16 sailing conditions are forecasted by numerical simulation of catamaran combining with wave data, the results show the presence of high-frequency components in each of the vibration response are both steady-state and high-proportion, relationship regularity conclusions between high-frequency component and frequency ratio are obtained, which provide a guideline in further study on wave-induced vibration in time domain.