The present invention relates to an acrylonitrile-styrene-acrylate (ASA) graft copolymer having a core-shell structure, and a method for manufacturing the same, wherein the core of the ASA graft copolymer is a multi-core rubber copolymer in which alkyl acrylate monomers are sequentially polymerized, and the shell is formed by graft-polymerizing a styrene-based monomer and an acrylonitrile-based monomer with the core. The ASA graft copolymer resin is manufactured by the steps of manufacturing the multi-core rubber polymer latex by sequentially polymerizing the alkyl acrylate monomers; and forming a shell layer by graft-polymerizing the styrene-based monomer and the acrylonitrile-based monomer with the multi-core rubber polymer. The ASA resin composition according to the present invention has excellent impact resistance, weather resistance, and dyeability properties.