In an electron-emitting device, an electron supplying layer for supplying electrons is composed of an n-GaN layer. An electron transferring layer for moving electrons toward the surface is composed of non-doped (intrinsic) AlxGa1−xN (0≦x≦1) having a graded composition for the Al concentration x. A surface layer is composed of non-doped AlN having a negative electron affinity (NEA). The electron transferring layer composed of AlxGa1−xN has a band gap which is enlarged nearly continuously from the electron supplying layer to the surface layer and a negative electron affinity or a positive electron affinity close to zero. If such a voltage V as to render the surface electrode side positive is applied, the band of AlxGa1−xN is bent, whereby a current derived mainly from a diffused current flows from the electron supplying layer to the surface layer through the electron transferring layer. Thereby excellent electron emitting characteristic is obtained.