The structure and electronic states of copper phthalocyanine (CuPc) on Cu(100) and Cu(110) were studied mainly using scanning tunneling microscopy/spectroscopy (STM/STS). We observed that the molecule adsorbs flat on Cu(100), and the lowest unoccupied molecular orbital (LUMO, e${}_g$) is shifted down to the Fermi level, which indicates a partially filled state. The inherent fourfold symmetry of the molecule remains intact upon adsorption, and thus, the degeneracy of LUMO is maintained on the surface. Conversely, the molecule adsorbs in a low-symmetry configuration on Cu(110) and preferentially forms a dimer. Thus, the degeneracy of LUMO is lifted, and the split LUMO is shifted below the Fermi level. We propose that the hybridization with surface d band plays an important role in the energy level alignment and its structure dependence for CuPc on Cu surfaces.