The embodiment of the invention provides a dynamic random access memory (DRAM) refreshing method and an apparatus thereof in order to reduce the refreshing cost of the DRAM and reduce the power consumption of a chip. The method comprises the following steps: a memory controller sends a first refresh command to a first refresh address counter on a first refresh cycle, and sends a second refresh command to a second refresh address counter on a second refresh cycle; and the first refresh address counter receives the first refresh command and then outputs a first row address in order to make a row address multiplexer refresh the memory cell of the first row address corresponding to the DRAM according to the first refresh cycle, and a second refresh address counter receives the second refresh command and then outputs an intermediate address in order to make the row address multiplexer refresh the memory cell of a second row address corresponding to the DRAM according to the second refresh cycle. The method and the apparatus can adopt different refresh cycles according to the difference of the data retention time of memory cell rows in order to reduce the refresh cost of the DRAM and the power consumption of the chip.