Abstract: A new numerical method for solving aerodynamic hybrid problem of fully three dimensional(3-D)flow in turbomachinery is presented.This method is based on non orthogonal coordinate system and contravariant velocity components and employs the approximate factorization multigrid scheme in conservative form.It has been proved that this scheme improves the numerical computation convergence speed and the computational precision. In the present hybrid solution method,the meridional positions(z,r)at all grid points are kept unchanged in the proecss of iterations.