A process for producing a polyether polyol with a content of 0.5 to 99.5% by weight of oxytetramethylene groups derived from tetrahydrofuran by copolymerizing tetrahydrofuran or a mixture of tetrahydrofuran and other cyclic ether copolymerizable therewith with a polyhydric alcohol having two or more hydroxyl groups per one molecule with the use of a heteropoly-acid and/or its salt as a catalyst, which comprises allowing 0.1 to 15 molecules of water per one heteropoly-anion to exist in the catalyst phase.The above-described polyether polyol is an industrially useful polymer which is a starting material for polyurethane to be used for spandex or a synthetic leather, etc.