The growth process of silicon on the Si(111)√3×√3-Ag surface (here after √3Ag surface) has been studied by scanning tunneling microscopy (STM). Islands of one bilayer thickness with infinite form and triangular geometry are observed for 0.32 ML(ML:1 ML=7.8×10¹⁴/cm²) deposition of silicon on the √3Ag surface. The orientation of two dimensional islands with triangular geometry is the same as that of unfaulted half unit of the Si(111)7×7 structure (here after 7×7 structure). The surface structure of the Si islands is characterized as the √3 structure by analysis of STM images of the island. It is believed that Ag atoms segregate on the deposited silicon islands and the island surfaces become the √3Ag structure. In comparison with densities of the islands on the 7×7 and the √3Ag surfaces, it is concluded that the diffusion coefficient of Si atoms on the √3Ag surface is about 60 times larger than that of Si atoms on the 7×7 surface. The value of the diffusion coefficient is independence on deposition rates. We also discuss a possibility of the Schwoebel effect on the √3Ag surface for Si atoms because populations of the islands at step edges of upper terraces are higher than those at lower step edges. [DOI: 10.1380/ejssnt.2009.763]