The two coordinate systems of cradle-type hypoid generator and free-form CNC machine tool by application disc milling-cutter to generate hypoid pinion tooth surfaces based on the modified-roll method were set up, respectively, and transformation principle and method for machine-tool settings between the two coordinate systems was studied. It was presented that finger milling-cutter was mounted on imagined disc milling-cutter and its motion was controlled directly by CNC shafts to replace disc milling-cutter blades effective cutting motion. Finger milling-cutter generation accomplished by ordered circular interpolation was determined, and interpolation center, starting and ending were worked out. Finally, a hypoid pinion was virtually machined by using CNC machining simulation software VERICUT.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.