Due to the downward closure property over uncertain data, existing solutions of mining all the frequent itemsets may lead an exponential number of results. In order to obtain a reasonable result set with small size, frequent closed itemsets discovering over uncertain data were studied, and a new algorithm called Normal Approximation-based Probabilistic Frequent Closed Itemsets Mining (NA-PFCIM) was proposed. The new method regarded the itemset mining process as a probability distribution function, and mined frequent itemsets by using the normal distribution model which supports large databases and can extract frequent itemsets with a high degree of accuracy. Then, the algorithm adopted the depth-first search strategy to obtain all probabilistic frequent closed itemsets, so as to reduce the search space and avoid redundant computation. Two probabilistic pruning techniques including superset pruning and subset pruning were also used in this method. Finally, the effectiveness and efficiency of the proposed methods were verified by comparing with the Possion distribution based algorithm called A-PFCIM. The experimental results show that NA-PFCIM can decrease the number of extending itemsets and reduce the complexity of calculation, it has better performance than the compared algorithm.