In this paper a new．approximate．method，which is called "The Conformational Counting Method”，for estimating the conformational entropy of polymer chains has been proposed．The method is applied to random self-avoiding walks on simple cubic lattice．In the range of chain step number n=7～19 the entropy data obtained by this method are consistent perfectly with their precise value and the deviation is smaller than 0.04％ (sample sizes～2，ooo)．In the range of n up to 26 of chains confined in a cubic box of side length 2 the entropy data are consistent very good also with their precise value obtained bv means of directly counting all conforma-tions．The deviation is smaller than 0.6％ (sample sizes～2，000)．In the range of n up to 2，100 of free chains

the entropy data confirm the renormalization group prediction：S/K=nlnμ+(γ-1)lnn+In Co where k is Bottzmann constant，μ=4.6838，γ=7／6 and Co=1.17．For all chain step number deviations are negative and within 0.8％ (sample size8～300)．The way to improve the accuracy is suggested.