The invention relates to a water-soluble polymer composition obtained by polymerizing in an aqueous polymerisation medium, which comprises degraded starch, at least following monomers: acrylamide and/or methacrylamide, and >2 mol-% of at least one unsaturated mono- or dicarboxylic acid(s) or salts thereof. The polymer composition has an anionic net charge at pH 7 and a dry solids content of >5 weight-%. The invention relates also to the use of the polymer composition for surface sizing of paper, board or the like as well as to a surface size composition comprising it.