The invention discloses a construction method of an obstacle-crossing wide-width swivel bridge closure section hanger formwork supporting system. The method includes the steps of firstly, lifting a temporary transverse beam through a winch installed on a box girder top plate close to one side of a closure section after a prefabricated half bridge is construction; secondly, after the temporary transverse beam is lifted in place, replacing the winch with a hanging rod for lifting the temporary transverse beam; thirdly, installing a bridge swivel; fourthly, putting down the temporary transverse beam, and hanging and installing a temporary longitudinal beam; fifthly, installing a bottom formwork system; sixthly, installing a flange plate and angel web support formwork system, installing the box girder bottom plate, web reinforcing steel bars and prestressing tendons, installing an inner mold support formwork system, installing top plate reinforcing steel bars and prestressing tendons, andfinally pouring concrete of the closure section; seventhly, detaching the inner mold support formwork system and the flange plate and angel web support formwork system; eighthly, detaching the bottomformwork system and the temporary longitudinal beam; and ninthly, detaching the hanging rod and the temporary transverse beam to complete the construction. A closure section hanger formwork supportingbody can be efficiently constructed, the construction fund is effectively saved, and construction safety is guaranteed.