Abstract We have observed the energy structure in the density of occupied states of graphene grown on n-type 6H-SiC (0 0 0 1). The structure revealed with photoelectron spectroscopy is described by creation of the quantum well states whose number and the energy position (E₁ = 0.3 eV, E₂ = 1.2 eV, E₃ = 2.6 eV) coincide with the calculated ones for deep (V = 2.9 eV) and narrow (d = 2.15 Å) quantum well formed by potential relief of the valence bands in the structure graphene/n-SiC. We believe that the quantum well states should be formed also in graphene on dielectric and in suspended graphene.