A method for eliminating bit line leakage current of a memory cell in random access memory devices comprises the steps of: periodically activating a pre-charge equalization circuit, which provides a pre-charge voltage to a pair of complementary bit lines of a memory cell, if the memory cell is in a self-refresh mode or a standby mode; and temporarily activating the pre-charge equalization circuit after the memory cell is refreshed if the memory cell is in the self-refresh mode or the standby mode.