A new method is proposed based on the position group contribution additivity for the prediction of melting points of covalent compounds. The characteristics of this method are the use of position distribution function, which could distinguish between most isomers including cis or trans structure of organic compounds. Contributions for hydrocarbons and hydrocarbon derivatives containing oxygen, nitrogen, chlorine bromine and sulfur, are given. Results are compared with those by the most commonly used estimating methods. The average derivation for prediction of normal melting temperature of 730 compounds is 14.46 K, compared to 29.33 K with the method of Joback, and 27.81 K with the method of Constantinou-Gani. The present method is not only more accurate, but also much simpler and more stable.