When a driving circuit of an anti-fuse memory device programs a selected anti-fuse memory cell, voltage differences between unselected bit lines and unselected anti-fuse control lines would be eliminated or decreased to an acceptable value by floating unselected anti-fuse control lines or by applying a second control line voltage to the unselected anti-fuse control lines. Leakage currents flowing from unselected bit lines through ruptured anti-fuse transistors of the anti-fuse memory device to the unselected anti-fuse control lines would be decreased or eliminated, and program disturbance would be avoided.