Method for producing a polyalkylene oxide

To improve the reactivity reduction of the composite metal cyanide complex catalyst in the case of using the low molecular weight initiator, it provides a method for producing in good productivity low cost to produce a polyalkylene oxide. The organic solvent and the composite metal cyanide complex catalyst presence, on the molecular weight of 300 or less initiator per hydroxyl group having at least one hydroxyl group, a method for producing a polyalkylene oxide to ring-opening addition reaction of alkylene oxide, initiation against sometimes charged alkylene oxide 100 parts by weight, and wherein the use of organic solvent is 500 to 1,500 parts by weight.