Abstract: The sales of on-line shopping follow the rule of long tail distribution, therefore the total sales of unpopular goods are very large. Recommendations for unpopular goods are as important as recommendations for popular goods. However, many existing recommendation methods only focus on the recommendations for popular goods, and assign an average weight of recommendation to unpopular goods which have small number of ratings, thus it is hard to bring unpopular goods to user's attention and the sales of unpopular goods are depressed. So it is very important to improve the weight of recommendation for unpopular goods. In this paper, a long tail distribution constrained recommendation (LTDCR) method is proposed for improving the weight of recommendation for unpopular goods appropriately. The weight of recommendation in LTDCR is calculated using similarity relationship among users, where the similarity relationship is determined by the similarity of users' behaviors and is propagated under the constraint of distrust relationship. In order to improve the weight of recommendation for unpopular goods, the weight of recommendation is constrained by the long tail distribution. An accurate description of long tail distribution is also given in this paper. The experimental results in dataset containing large number of unpopular goods show that LTDCR need fewer training set to improve the effectiveness of recommendations for unpopular goods.