The technology of data mining becomes important in recent years, and it is generally applied to commercial forecast and decision supports. Association rules mining algorithms play the important role in the field of data mining. Many of association rules mining algorithms were proposed to improve the efficiency of data mining or save the utility rate of memory. Our major study also tries to improve the efficiency of association rules mining algorithms. In this paper our major study is to improve the defects oft he GDA algorithm. Although GDA algorithm was one of the most efficient algorithms, but it still has two serious problems; in the first place, GDA algorithm can’t mine the transactions of databases whose record length is very long; in the second place, GDA algorithm isn't very efficient at utility rate of the memory when it must store lots of unnecessary itemsets at one phase. Therefore, the GDA algorithm is not very practical. Based on above the reasons we propose a new algorithm - GRA (Gradation Reduction Approaches) that is improved from GDA algorithm. One of the characters of the GRA algorithm is the gradation reduction mechanisms because it can reduce lots of infrequent itemsets; the GRA algorithm is very suitable to mine the transactions of databases whose record length is very long. In the mining procedure, the GRA algorithm doesn’t generate any candidate itemset to find association rules quickly. Besides, the GRA algorithm through gradation reduction mechanisms only generate those itemsets which are the most possible to be the frequent itemsets. So, the GRA algorithm can’t waste lots of memory spaces to store infrequent itemsets; it can efficiently increase the utility rate of memory. The size of the databases in the real world is always greater than the size of the memory. In order to solve this problem, we propose a modifying algorithm - GRA-M (Gradation Reduction Approaches - Modifying); it divides a large database into many sub-databases and mines association rules from those sub-databases. The GRA-M algorithm only scans database four times and will not be affect by the length of frequent itemsets. The GRA-M algorithm avoids wasting a lot of I/O time and increases the efficiency and the practicability in application.