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How to generate the candidate itemsets, how to compute the supporting number of itemsets, how to reduce the size of candidate itemsets and how to decrease the scanning times of transaction databases, are four capital technique difficulties of association rules mining. In this paper, we have presented an new idea that transforms the data structure of transaction databases to the directed graph, and applies the directed itemsets graph to store the relevant information of frequent itemsets of transaction databases, and puts forward trifurcate linked list storage structure of directed itemsets graph, and provides mining algorithm of complete frequent itemsets based on the directed itemsets graph. So the four capital technique difficulties mentioned above are resolved efficiently.