After introducing fractional damping into classical Duffing oscillator, a high efficient numerical algorithm was deduced. The research on the fractional Duffing oscillator indicates that, decreasing the damping fractional order, the time period of oscillator changes and further goes to chaos. Under the external excitation forces of different frequencies, the strange attractor can be found at a lower frequency. The fractional Duffing oscillator comes into chaotic state earlier than the integral classical Duffing oscillator. The smaller the fractional order, the smaller the critical excitation needed to become chaos.