In an anti-fuse memory includes a rectifier element of a semiconductor junction structure in which a voltage applied from a memory gate electrode to a word line is applied as a reverse bias in accordance with voltage values of the memory gate electrode and the word line, and does not use a conventional control circuit. Hence, the rectifier element blocks application of a voltage from the memory gate electrode to the word line. Therefore a conventional switch transistor that selectively applies a voltage to a memory capacitor and a conventional switch control circuit allowing the switch transistor to turn on or off are not necessary. Miniaturization of the anti-fuse memory and a semiconductor memory device are achieved correspondingly.