Abstract: An air foil bearing assembly is provided. The air foil bearing assembly includes a bearing housing that has a hollow into which a rotary shaft is fitted and a slot of which both ends are open toward front and rear sides formed on an inner circumference surface of the hollow. A bump foil is provided to have a combining portion inserted to the slot and disposed in the inner circumference surface of the hollow. A top foil having a combining portion is inserted to the slot and is disposed in an inner side of the bump foil. A stopper is disposed on one of the combining portions of the bump foil or the top foil to prevent the combining portion of the bump foil or the top foil from being displaced from the slot toward the front and rear sides.