In this paper,the sharp estimates of all homogeneous expansions for f are established,where f(z)=(f1(z),f2(z),…,fn(z))'is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in Cn and theorem for a k-fold symmetric quasi-convex mapping are established as well.These results show that in the case of quasi-convex mappings,Bieberbach conjecture in several complex variables is partly proved,and many known results are generalized.