In this article．the normal distribution is generalized to be a three．parameter pro-bability density function which is called the semi-normal distribution (SND)．The log semi-normal distribution derived from SND is a molecular weight distribution func-tion with a wide range of applications since the graph of this distribution function is represented by a network which covers a vast region containing the curved angular zone formed by Schulz distribution and log normal distribution in the continuum of molecular weight distributions set by W．E．Gloor．The SND has some good eharac-teristics as the normal one thus it is adaptable to GPC results especially more advan-tageous for chromatogram with asymmetric peak．Some useful equations，curves and tabulated values of the special function are in this atticle．With the aid of them the various average moleeular weights ean be easily figured out．It is also possible to calculate the parameters of a distribu-tion from three molecular weight averages．