A slide member (26) is externally fitted to an outer peripheral surface of an outer ring (20) configuring a tip side bearing (9a) for supporting a tip portion of a worm shaft (6a) so as to be displaceable in an axial direction. A first inclined cylindrical face portion (32) which is an inclined surface disposed on an outer peripheral surface of the slide member (26), and a second inclined cylindrical face portion (30) which is an inclined surface disposed on an inner peripheral surface of a guide member (28) internally fitted and fixed to a holding hole (10a) of a housing (3a) are fitted to each other so as to be slidable in an inclined direction of the respective inclined cylindrical face portions (32, 30). An elastic ring (29) which biases a bearing holding member (26) against to one side in the axial direction is disposed. This realizes a structure which can shorten an axial dimension of a tip side portion of the worm shaft in an electric power steering device including biasing means for minimizing backlash in a meshing portion of a worm reduction gear.