Abstract: The surface states of semi-infinite one-dimensional photonic crystal composed of positive and negative refractive materials are theoretically investigated with the method of the transmission matrix and Bloch theorem. It is found that when the photonic crystal is adjacent to a dispersive medium background and the average refractive index is equal to zero, the surface states can be sensitively changed in a large frequency range while the thickness of the cap layer is changing. The electric field distributions of two surface states with the same incident angle and different frequency are discussed. The result shows that the surface state which is far from the band edge has a smaller local length.