We report localized surface waves at the interface between linear dielectric and centrosymmetric photorefractive (CP) crystals. Adjusting the values of the guiding parameter δ and the propagation constant b, we can easily get three types of surface waves: delocalized surface waves, shock surface waves, and localized surface waves. When the difference between b and δ exceeds a certain threshold value, the localized surface waves can form at the interface between linear dielectric and CP crystals. For positive δ values, the part of the energy of localized surface waves concentrated in the nonlinear CP crystals is always higher than that in the linear dielectric, and increases monotonically with b. The stability properties of the localized surface waves are investigated numerically and it is shown that they can be stable. In a given system, the orders and waveforms of localized surface waves are controlled by adjusting the variable parameters which determine the strength of nonlinear effects.