We have grown high density Co dusters with a narrow-sized distribution on the Si3N4(0001)-(8 × 8) surface. In the submonolayer regime, Co clusters tend to keep a certain size (～ 1.45 nm in diameter) irrespective of coverage.With increasing coverage above 0.92 ML, two new clusters with certain but larger sizes are formed. This novel growth behaviour can be explained by the quantum size effect [Phys. Rev. Lett. 90 (2003) 185506]. It is found that the Co cluster size distribution can be improved by post annealing. Even at high temperature (700℃ ), no reaction of Co with Si3N4 is observed, indicating that Si3N4(0001)-(8 × 8) is a promising substrate for growth of magnetic nanostructures.