PROBLEM TO BE SOLVED: To obtain an admixture relieving or unnecessitating compaction at the time of concrete placing when added to fresh concrete by incorporating an acrylamide polymer contg. units derived from three kinds of specified compds. SOLUTION: This high flowability admixture is made of a polymer contg. 10-98wt.% units derived from a compd. represented by formula I (where R is H or CH3 ), 1-60wt.% units derived from a compd. represented by formula II (where R is H or CH3 , R is 1-4C alkylene, X is CONH or COO and X is H, an alkali metal, an ammonium salt or an org. ammonium salt) and 1-40% units derived. from a compd. represented by formula III (where R is H or CH3 , X is CN, COOR , COR , etc., and R is H, an alkali metal, an ammonium salt, 1-4C alkyl, etc.). When this admixture is added to fresh concrete, high flowability, high fillability and high separation resistance are imparted and compaction at the time of concrete placing is relieved or unnecessitated.