In through-feed grinding workpieces by grinding stones rotating around the axes of spindles, the spindles are tiltably held by elastic holding means around tilt axes substantially orthogonal to the direction of exit and entrance of the workpieces with respect to the grinding stones. When a grinding loads are imposed on the entrance sides of the grinding stones, the spindles are tilted by offset loads around the tilt axes against the force of urging means in such a manner that the axial displacement and the exit displacement of the grinding stone due to the offset load are substantially the same. The grinding stones are reset around the tilt axes by the elastic holding means immediately before the end of processing at which time the axial displacement is smaller. This makes it possible to reduce the number of defectively ground articles coming from the through-feed grinding and reduce the wear in the grinding stones.