A polycarboxylic acid-based polymer for a cement admixture, wherein the polymer contains 2 to 90% by mass of a constitutional site represented by the general formula: wherein R 1, R 2 and R 3 are the same or different, and represent a hydrogen atom, a methyl group or -(CH 2)zCOOM 2, Z represents a number of 0 to 2, wherein -(CH 2) Z COOM 2 may form an anhydride with -COOM 1 or -(CH 2) Z COOM 2, and M 1 and M 2 are the same or different, and represent a hydrogen atom, an alkali metal atom, an alkaline earth metal atom, an ammonium group or an organic amine group; the polymer contains 2 to 98% by mass of a constitutional site represented by the general formula: wherein R 4 and R 5 are the same or different, and represent a hydrogen atom or a methyl group, AO represents one kind of an oxyalkylene group of a carbon number of 2 to 4, or a mixture of two or more kinds of the oxyalkylene groups and, in the case of two or more kinds of the groups, they may be added in a block manner or a random manner, x represents a number of 0 to 2, y represents 0 or 1, n represents the average addition mole number of the oxyalkylene group, and is a number of 1 to 300, and R 6 represents a hydrogen atom or a hydrocarbon group of a carbon number of 1 to 20; the polymer has a lower molecular weight side area ratio P as defined by the following conditions to of 50 to 87%: Measurement is performed by gel permeation chromatography, and a GPC chart is obtained; A baseline of the GPC chart is drawn, the intersection point between the higher molecular weight side of the GPC chart and the baseline is expressed by Lh, and the intersection point between the lower molecular weight side of the GPC chart and the baseline is expressed by Ln; The intersection point between a line which passes through the peak Mp (when there are plural peaks, the peak on a lowest molecular weight side) of the GPC chart and is vertical to the baseline, and the baseline is expressed by Lp; The middle point between Lp and Lh is expressed by Lm; The area on the lower molecular weight side than Lp is expressed by P0, and the area on the higher molecular weight side than Lm is expressed by Q0 in the GPC chart; The lower molecular weight side area ratio P (%) is defined as P = (P0×100)/(P0+Q0); and the polymer has a peaktop molecular weight Mp of 10000 to 40000, wherein the peaktop molecular weight represents the molecular weight corresponding to the highest position in the curve plotted in the GPC chart, obtained under GPC measuring conditions as defined in the description. Measurement is performed by gel permeation chromatography, and a GPC chart is obtained; A baseline of the GPC chart is drawn, the intersection point between the higher molecular weight side of the GPC chart and the baseline is expressed by Lh, and the intersection point between the lower molecular weight side of the GPC chart and the baseline is expressed by Ln; The intersection point between a line which passes through the peak Mp (when there are plural peaks, the peak on a lowest molecular weight side) of the GPC chart and is vertical to the baseline, and the baseline is expressed by Lp; The middle point between Lp and Lh is expressed by Lm; The area on the lower molecular weight side than Lp is expressed by P0, and the area on the higher molecular weight side than Lm is expressed by Q0 in the GPC chart; The lower molecular weight side area ratio P (%) is defined as P = (P0×100)/(P0+Q0); and