There are provided an admixture for cement which enhances water reducing property and flowability of a cement composition, and is excellent in slump retaining performance to retain the flowability with time, a polycarboxylic acid-based polymer for an admixture for cement suitable therefor, a producing method thereof, and a cement composition. One admixture for cement of the present invention contains copolymers (A) and (B) as an essential component, weight average molecular weights (AMw and BMw) of copolymers (A) and (B) are AMw>BMw, or peaktop molecular weights (AMp and BMp) of copolymers (A) and (B) are AMp>BMp. Another admixture for cement of the present invention contains a polycarboxylic acid-based polymer having a lower molecular weight side area ratio P of 50 to 87%.