An apparatus for power steering of a vehicle, comprises: a worm gear arrangement including a worm shaft and a worm wheel engaged with the worm shaft; a bearing to support the worm shaft rotatably; a gear housing structure enclosing the worm gear arrangement, and defining a holder receiving portion; and a holder member arranged to hold the bearing, and fit movably radially in the holder receiving portion. A biasing mechanism urges the holder member or the bearing in a nearing direction toward the worm wheel. A buffer member is arranged to be compressed by the holder member when the holder member is moved in the nearing direction to buffer collision of the holder member in the holder receiving portion. The buffer member is set to have an elastic force smaller than the biasing elastic force of the biasing mechanism.