A sealing structure for a refrigerator is provided. The structure includes a gasket formed at a door of the refrigerator and at least two air pockets provided in the gasket. There is at least one connector, which separates the at least two air pockets from each other, and first convection cut-off members provided inside of the at least two air pockets. Additionally, the seal structure includes an inner case provided at an interior side of the refrigerator; a door liner, which lines the door, provided at an interior side of the refrigerator; and an air dam provided between the inner case and the door liner. Further, second convection cut-off members are provided in the air dam.