An improved anchor agitator is provided for performing uniform and effective stirring of the fluidized bed zone of a polymerization vessel in a gaseous phase polymerization, especially of olefins such as ethylene and propylene. The anchor agitator includes at least two pairs of arms provided on a rotating shaft in mutually crossing positions. A pair of main blades is provided at opposite outward end portions of one pair of arms and at the opposite outward portions of each remaining pair of arms a pair of subsidiary blades is provided. The main blades and subsidiary blades extend substantially parallel along the axis of the rotating shaft and each pair of blades is located substantially equidistant from the axis of the rotating shaft. The pair of main blades is located farther from the axis of the rotating shaft than the subsidiary blades. The main blades and subsidiary blades are uniquely designed to avoid the formation of coherent crusts or lumps near the inner wall of the polymerization vessel and to avoid formation of a vortex formed centrally in the fluidized bed zone of the vessel in the vertical direction of the zone. The unique angular relationships and distance relationships of the main blades and subsidiary blades also avoid the likelihood of vibration due to mechanical imbalance of the agitator while at the same time allowing the agitator to be easily designed and built.