The disclosure provides a cell culture system and a serum-free method for cultivating cells. The cell culture system includes a substratum, wherein the substratum has a surface. A polymer is disposed on the surface of the substratum, wherein the polymer is prepared by polymerizing a first monomer with a second monomer. The first monomer has a structure as represented by Formula (I), and the second monomer has a structure as represented by Formula (II): wherein, R1 is hydrogen or methyl; R2 is methyl, ethyl, or —CH2CH2OCH3; R3 is hydrogen or methyl; and, R4 is hydrogen, —CH2CH2OCOCHCHCOOH, —CH2CH2OCOCH2CH2COOH, or —CH2CH2COOH.