To obtain a water-soluble polymer capable of manifesting functions such as viscosity-improving property, stickiness or the like wherein the functions are not lost even in the presence of high concentration salts or multivalent metal ions and useful for a viscosity improver, a viscosity modifier, a thickener, a soil conditioner or the like.

This polymer comprises recurring units of formula I (R1 is H or methyl; n is an integer of 2-4) and recurring units of formula II (R2 is H or methyl; M is H, a univalent metal or the like) wherein the molar ratio of the structural unit of formula I to the structural unit of formula II is (5:95) to (95:5) and the polymer has ≥2,000,000 weight average molecular weight and is obtained by copolymerization of a mixture of a monomer giving the units of formula I (e.g. N-vinylpyrrolidone) and a monomer giving the units of formula II (e.g. acrylic acid). The weight average molecular weight is measured by gel permeation chromatography and expressed based on sodium polyacrylate standard.