To provide a serum-free medium providing improved cell-proliferative properties in a serum-free medium, and hardly providing risk of mixing of an infectious factor.

The serum-free medium contains an artificial polypeptide (P) having at least one minimum amino acid sequence (X) with cellular adhesiveness in one molecule. Preferably, (X) is Arg Gly Asp sequence. Preferably, (P) has at least one assistant amino acid sequence (Y) in one molecule of the (P). Preferably, (P) has a structure obtained by alternately chemically bonding an amino acid sequence containing an interstitial amino acid sequences (Z) and (Y) at both the terminals of (X).