We have investigated the dynamics of the Lorenz system under quasiperiodic driving. When the forcing amplitude is increased to certain critical value，the dynamics changes fundamentally. Therefore a new mechanism for the creation of the strange nonchaotic attractor is advanced in this paper. When the forcing amplitude is increased, the strange attractor is replaced by a strange nonchaotic attractor, eventually the phase space is suppressed into an invariant quasiperiodic torus. Numerical results show that the critical amplitude of the force is roughly proportional to the Rayleigh parameter, but slightly influenced by its frequency.