In this paper, following Zhao N. & Wu H.M.'s paper(1995), we analysis the "sharp" estimate of the rate of entropy dissipatin of the fully discrete MUSCL type Godunov schemes by the general compact theory introduced by Coquel-LeFloch(1991,1993), and find: because of small viscosity of the above schemes, in the vicinity of shock wave, the estimate of the above schemes is more easily obtained, but for rarefaction wave,we must impose a "sharp" condition on limiter function in order to keep its entropy dissipation and its convergence.