A novel method is proposed for simulating the motion of flexible fibers in a 3D swirling flow, where the fiber is modeled as a chain of beads connected through mass-less rods. The bending and twisting displacements of the successive beads are used to represent the deformation of the fiber. In addition, the drag and shear-induced lift forces are considered in the proposed model as parts of external loads acting on the fiber in the swirling flow. In the numerical simulation, the spiral motion trajectory of the fiber is observed to have a springy or helical configuration. The numerical results are validated by experimental visualization using high-speed photography.