A hole expansion process is an important process in producing a hub-hole in a wheel disc of a vehicle. In this process, the main parameter is the formability of a material that is expressed as the hole expansion ratio. In the process, a crack is occurred in the upper edge of a hole as the hole is expanded. Since prediction of the forming limit by hole expansion experiment needs tremendous time and effort, an appropriate fracture criterion has to be developed for finite element analysis to define forming limit of the material. In this paper, the hole expansion process of a hub-hole is studied by finite element analysis with ABAQUS/standard considering several ductile fracture criteria. The fracture mode and hole expansion ratio are compared with respect to the various fracture criteria. These criteria do not predict its fracture mode or hole expansion ratio adequately and show deviation from experimental results of hole expansion. A modified ductile fracture criterion is newly proposed to consider the deformation characteristics of a material accurately in a hole expansion process. A fracture propagation analysis at the hub-hole edge is also performed for high accuracy of prediction using the new fracture criterion proposed.