Provided by this invention are an acrylamide polymer which has a weight-average molecular weight (a) of from 1,500,000 to 10,000,000 and a weight-average inertial radius (b) of from 30 to 150 nm, the ratio (b)/(a) of the weight-average inertial radius (b) to the weight-average molecular weight (a) being 0.00004 or smaller; and an aqueous solution of an acrylamide polymer which solution has a polymer concentration ranging from 22 to 60%, a Brookfield viscosity at 25.degree. C. of 50,000 cps or smaller and a weight-average molecular weight of from 500,000 to 10,000,000. They are useful as paper strength agents.