A cross point nonvolatile memory device capable of suppressing sneak-current-caused reduction in sensitivity of detection of a resistance value of a memory element is provided. The device includes perpendicular bit and word lines; a cross-point cell array including memory cells each having a resistance value reversibly changing between at least two resistance states according to electrical signals, arranged on cross-points of the word and bit lines; an offset detection cell array including an offset detection cell having a resistance higher than that of the memory cell in a high resistance state, the word lines being shared by the offset detection cell array; a read circuit (a sense amplifier) that determines a resistance state of a selected memory cell based on a current through the selected bit line; and a current source which supplies current to the offset detection cell array in a read operation period.