We theoretically study the nonlinear surface wave propagation at the interface between superconductor media and nonlinear metamaterials. The dispersion equation is analytically derived and solved numerically. Moreover, we present the power for the propagating waves at the interface. The results display different behaviors of the propagating waves as the nonlinear term or temperature is tuned. These results indicate that this structure can have potential applications in superconductor waveguide devices and integrated optics.