The invention discloses an anti-deformation hoisting device for a building air duct and a hoisting method of the anti-deformation hoisting device for the building air duct. According to the anti-deformation hoisting device for the building air duct, inner supporting devices are installed on the inner wall at air duct hoisting points and avoid the situation that because the air duct deforms in the lifting process, the installation quality is influenced. According to the anti-deformation hoisting device for the building air duct and the hoisting method of the anti-deformation hoisting device for the building air duct, the multiple hoisting points are adopted, stress analysis is conducted on the air duct before hoisting so that possible deformation in the air duct hoisting construction process can be selected and calculated, and the number and the positions of the hoisting points, the hoisting torque needed at each hoisting point and the weight distribution positions of the air duct are determined; the situation that because the air duct is stressed and deforms, the installation precision is influenced can be guaranteed to be avoided in the hoisting process; and a proportional hydraulic system is adopted, the stress condition of a deformation detection oil cylinder is fed back through an oil pressure sensor, a laser range finder is used for guaranteeing that the hoisting process is stable, the air duct is prevented from inclining in the hoisting process, and the height differences among all the hoisting points are reasonably controlled.