Abstract: This paper researches the dynamic response characteristic of the cycloid bevel gear under a wide range of operation speed and torque,and proposes a new method of semi-analytical FEM.The new method can precisely present the key factors of the gear tooth such as the tooth geometry and tooth contact stress,which influences the dynamic characteristic of the cycloid bevel gear significantly.Different from the conventional method,the non-line factors such as the static transmission error,time-varied stiffness and meshing frequency variation are no longer considered as the excitation.However,every time step of gear meshing is considered to calculate the dynamic contact stress and dynamic transmission error,and finally present the non-line vibration characteristic of cycloid bevel gear.