We investigate a thin Sn film grown at elevated temperatures on the fivefold surface of an icosahedral AlCuFe quasicrystal by scanning tunneling microscopy (STM). At about one monolayer coverage, the deposited Sn is found to form a smooth film of height consistent with one-half of the lattice constant of the bulk Sn. Analysis based on the Fourier transform and autocorrelation function derived from high-resolution STM images reveals that Sn grows pseudomorphically and hence exhibits a quasicrystalline structure.