In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density- weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flows in divergent curved channels was carried out by means of parabolized computation method. The calculating results were used to analyze and investigate the aerodynamic performance of stator cascades in compressors preliminarily.