The grinding efficiency can be improved by use of a vertical roller mill, while reducing the energy consumption and improving the product quality. The disclosed cement clinker grinding apparatus comprises a closed circuit for conveying the ground material from the vertical roller mill (21) to the external separator (28) by the bucket elevator (29), for classifying the conveyed material into coarse powder and fine powder, and further for returning the classified coarse powder into the vertical roller mill (21). That is, a part of the ground material conveyed by the bucket elevator (29) is divided by the distributing damper (32) and then directly returned to the vertical roller mill (21). Since the ground material are not conveyed by air flow conveyance (i.e., air sweep), it is possible to prevent an increase of power consumption of the suction fan (31).; Further, since a part of the ground material is distributed by the distributing damper and then further ground again by the vertical roller mill, it is possible to obtain an optimum particle size distribution of the cement products, so that the cement quality can be improved.