It is well known that the task of finding frequent itemsets in large database is the bottleneck problem in the research of association rules mining. A new algorithm for mining frequent itemsets is proposed in this paper. Based on the graph theory, the algorithm converts the origin transaction database to an itemsets adjacent lattice in the preprocessing, where each itemset vertex has a label to save its support. The algorithm changes the complicated task of mining frequent itessets in the database to a simpler one of searching vertex in the lattice, which can speed up greatly the mining process. Furthermore, to compute the support of each itemset, the algorithm uses a vertical tid-list database format, where each itemset is associated with a list of transactions in which it occurs. At the end, we carried out the algorithm, and analyzed the result of the experiment