A torsional vibration model of the K- H- V cycloid steel ball transmission system is established with considering the direction changing of engagement force and the multi- balls engagement in transmission process. By analyzing the position relationships of each engagement force and the displacement relationships of each component,the governing differential equations of the system and the dimensionless equivalent engagement rigidities of each transmission disc are derived. And then,the frequency spectrum of the engagement rigidity excitation is analyzed,and the influences of the system transmission ratio and the cycloid curtate coefficient to the engagement rigidity excitation are discussed. At last,the natural frequency,the principal mode and the steady- state response of system are calculated. The results show that the cycloid steel ball transmission system is a parametric vibration system. The engagement rigidity excitation between the center disc and the planetary disc is a periodic and time- variant function,and the high- order harmonic components are included in the frequency spectrum.