An adjustable supporting frame is composed of a base, a turnable arm, and a face engaging part. The base has a base central hole, and a base ring with engaging teeth on an end thereon. The turnable arm further is composed of an inner arm, an outer arm, and a teeth shaft engaging both of the arms together. The inner arm at an end thereof is corresponding to the base ring and has engaging teeth to mesh with the teeth on the base ring. The other end of the inner arm has a sleeve with an inner through hole. The outer arm at an end thereof has engaging teeth and at the other end thereof has outer plates. One of the outer plates has engaging teeth. The face engaging part engages with the outer arm by way of a screw rod, has a face ring with engaging teeth to mesh with teeth on the outer arm.