A variable and reversible resistive element includes a transition metal oxide layer, a bottom electrode and at least one conductive plug module. The bottom electrode is disposed under the transition metal oxide layer. The conductive plug module is disposed on the transition metal oxide layer. The conductive plug module includes a metal plug and a barrier layer. The conductive plug is electrically connected with the transition metal oxide layer. The barrier layer surrounds the metal plug, wherein the transition metal oxide layer is made by reacting a portion of a dielectric layer being directly below the metal plug and a portion of the barrier layer contacting the portion of the dielectric layer, wherein the dielectric layer is formed on the bottom electrode. Moreover, a non-volatile memory device and methods for operating and manufacturing the same is disclosed in specification.