This paper presents a kinematic model to produce multifluted drills on a six-axis CNC tool-grinding machine. There are three special features of the proposed model. The first is the use of Denavit-Hartenberg notation to establish the ability matrix of a six-axis CNC tool-grinding machine. The second feature, the concept of a virtual hollow grinding wheel and virtual solid dresser, is invented to allow flutes and flanks to be machined by a single grinding wheel in one setup, thus improving manufacturing precision and lowering production costs. Thirdly, we present configuration matrices to express grinding wheel positions and orientations during machining of flutes and flanks. NC data equations are obtained by equating corresponding elements of the ability matrix and the configuration matrices of the grinding wheel. To verify the proposed methodology, a designed three-fluted drill was machined on a six-axis CNC tool-grinding machine. This paper combines the activities of drill design and manufacturing, making the production process more flexible, automatic, cost efficient and controllable.