A refrigerator is provided which selectively opens or closes an inner cover according to the closing or opening of an auxiliary door. The refrigerator includes a refrigerator door to open or close a refrigerator storage chamber, a door storage space provided at an inner side of the door, an access opening formed through the door to allow a user to take out items stored in the door storage space from the outside, the auxiliary door mounted at an outer side of the door to open or close the access opening, an inner cover mounted at the inner side of the door in an openable manner to separate the door storage space from the storage chamber, and an inner cover opening/closing device to close the inner cover when the auxiliary door is opened and to open the inner cover when the auxiliary door is closed.