This paper presents a novel method to generate three-axis CNC tool paths for machining freeform surfaces based on a preferred feed direction field. This research was initiated from a fluid dynamics behavior that the energy loss can be reduced when the streamlines of fluid and the small grooves on a surface are in the same directions. In this research, the fluid streamlines above the surface are defined by a collection of vectors. These vectors are regularized into a grid of vectors, and these regularized vectors are further projected onto the tangent planes of a grid of points on the surface to create the preferred feed direction field. Based on the parametric model of the surface, the vectors on the tangent planes of the surface are mapped into vectors in the parametric domain. A scalar function is constructed such that the isolines of this scalar function and the preferred feed direction vectors in the parametric domain are in the same directions. A group of isolines of the scalar function are identified and these isolines are mapped back onto the 3-D surface as the created tool paths considering the tolerance requirement. The developed method has been applied to generate the tool paths for machining surfaces of a compressor blade.