PURPOSE: To proudce a polyurethane polymer excellent in low-temperature properties and elastic recovery, by reacting an organic diisocyanate with a specified, active hydrogen-containing compound.

CONSTITUTION: 1mol of a polyether-diol obtained by cation ring-opening polymerization of 3-methyloxetane is reacted with 1W60mol of a 6W8C saturated aliphatic lactone in the presence of an organotitanium compound catalyst to obtain a saturated aliphatic lactone-modified diol (B) of formula I [wherein A is a 2-methyl-1,3-propylene group of formula II, B is a 1,4-butylene group of formula III, l+m=6W140, l/m=10/90W100/0 (molar ratio), Y is a bivalent residue derived by removing an ester bond from a 6W8C saturated aliphatic lactone ring, and p and q are positive numbers satisfying the relationship: 1≤p+q≤60]. An organic polyisocyanate (A) is reacted with a mixture at least 60wt% component B and a compound having at least two active hydrogen atoms in the molecule.