A catalyst for internal combustion engine exhaust purification without frequently switching to a rich burn mode. The catalyst includes a catalyst A containing an NOx absorbing substance and an NOx reducing catalyst, a catalyst B containing a hydrogen adsorption substance and a hydrogen oxidizing catalyst, an electron conductive substance C, and an ion conductive substance D. Electrons move between the catalyst A and the catalyst B through the electron conductive substance C, ions move through the ion conductive substance D, and an electrochemical reducing reaction and an electrochemical oxidizing reaction respectively occur on the catalyst A and on the catalyst B. Therefore, it is possible to quickly reduce the adsorbed NOx using the adsorbed hydrogen without depending on the atmosphere.