Considering a non-feedback mechanism of action，the present paper shows that the steady forcing induces amplitude death in chaotic system by investigating the bifurcation figures and the spectrum of Lyapunov exponents of the R?ssler oscillator. The manner, which is very similar to that in coupled limit cycles or coupled R?ssler system, is from periodic to an equilibrium point of the forced system. Furthermore，we investigate the time series of the forced system, and find that when the strength of the forcing is beyond a critical constant，the states of the system present the periodic dynamics with a small amplitude or rest alternately.