Poly(alkylene oxide) which does not contain any metallic component and does not leave an odor is prepared simply and efficiently, by a process using a polymerization initiator which does not cause any problems in preparing and handling in the preparation of the polyalkylene oxide by polymerizing an alkylene oxide compound, and does not require special treatment before the initiation of the polymerization. In the process, the alkylene oxide compound is polymerized in the presence of a phosphine oxide compound represented by the formula (1): wherein Rs are the same or different and each represents a hydrocarbon group having 1 to 10 carbon atoms, and x represents an amount of water molecules contained in terms of a molar ratio and is within a range from 0 to 5.0. If desired, the alkylene oxide compound can be polymerized in the presence of said phosphine oxide compound and an active hydrogen compound selected from water or an organic compound having a partial structural formula -OH or -NH-.