Propylene oxide is added to an active hydrogen compound in the presence of an alkali metal hydroxide catalyst in an amount of from 0.05 to 0.5 mole per mole of the active hydrogen compound at a reaction temperature of from 60 to 98.degree. C. at a reaction pressure less than or equal to 4 kg/cm.sup.2 to prepare a polyoxyalkylene polyol which has a hydroxyl value of from 10 to 35 mg KOH/g, a monool content less than or equal to 15 mol %, a Head-to-Tail bond selectivity greater than or equal to 96 percent, and low viscosity. A polymer polyol is prepared by polymerizing an ethylenically unsaturated monomer in the polyoxyalkylene polyol. A flexible polyurethane foam is prepared by reacting the polyoxyalkylene polyol or the polymer polyol with an organic polyisocyanate compound in the presence of a foaming agent, a catalyst, a surfactant, a crosslinking agent and other additives. The thus-obtained polyurethane foams have less closed cells and are more excellent in properties such as hardness, humid aged compression set and impact resiliency.