Crane-support apparatus for mounting a tower crane onto a side of a high-rise building under construction, enabling ascending of the tower crane according to the upwards progression of the building construction, including a chassis configured to support a climbing frame of the tower crane mast, and at least one reinforcement element. A distal end of the chassis is hingedly attached to the distal end of the reinforcement element. In a deployed, support mode, the chassis is aligned in a horizontal position, and the reinforcement element is aligned in a slanted position. In a folded, mobilization mode, the chassis and the reinforcement element are configured to be pulled by at least one lifting cable at the distal end of the chassis and the reinforcement element with the chassis and the reinforcement element hingedly folded and aligned in vertical positions. A method for using the apparatus in both modes is also provided.