Chatter in machine is gained more and more attention because of its occurrence results in poor surface finish, promotes wear of the tool and hamper productivity[1-3].The shifted Chebyshev polynomials and Floquet theory are adopted for the prediction chatter stability and bifurcation in milling[4-5].The stability lobes diagram is obtained.The stability in milling can well be predicted by the lobes diagram.The muliti-periodic and Hopf bifurcations are detected by the Eigen-values analysis.The result shows that the stability solution of the system transform from the stable equilibrium point to the limit cycle oscillatory after multiple cycle bifurcation, and it transforms to the quasi-periodic oscillation after Hopf bifurcation.The numerical result of the Poincaré section proves that the occurrence of the quasi-periodic oscillation.