This paper gives an efficient form of multiple-grid scheme and presents a"prediction-correction " method for processing the boundary conditions on a solid wall. The conver-gency and the stability of the scheme can be further improved by using local time stepping and residual smoothing. Finally

two-dimensional inviscid transonic cascade flows are calculated. The comparisonbetween the calculated and the measured results shows that this scheme possesses very fast convergence speed and satisfactory accuracy.