Abstract: An innovative method for calculating steady transonic viscous flows around an arbitrary airfoil with small separation bubble is presented. The concept of inviscid-viscous interaction makes it possible to calculate complex transonic flow field at less cost and computer storage.The inviscid flows are governed by the conservative full potential e-quations and solved by a fast algarithm. The flow field around the airfoil is transformed into the inner of the unit circle by the conformal mapping, in which the FFT technique is used. The boundary layer equations are numerically solved using the C-S-K box method. The inverse method on boundary layer equations is used to avoid the Goldstein Singularity at the separation point. Turbulent flows are simulated by simple vortex-eddy, model.Two examples on transonic viscous flows around NACA64A010 airfoil with free stream Mach number 0.8 and the angles of attack 4°and 3.5°,respectively, are calculated. The agreement between numerical and experimental results is very well.