Abstract: A new kind of high-order Godunovian scheme is suggested here, inwhich the hyperthesis of piece-wise linear or parabolic interpolation polynomial[9],[10]to construct the distribution with the discontinuity on net boundary is improved in this paper by introducing a piece-wise boundarylayer distribution. This kind of distribution is piece-wise montone and differentiable,so it is unneseccery to check the monotonuity like in PPM and MUSCL schemes.The new scheme called PBLM has hihg-order accuracy the same as PPM scheme, even on the points on which the accuracy only has 1-order in PPM scheme. The results of l-dimmensional shock tube show that the spread of shock in PBLM is thiner than that in PPM and the computational time is equivalent. Just as PPM,for PBLM scheme about 2%-4% oscillations occur behind the shock. The additional dissipation should be added.