Using Maxwell′s equations, surface modes in a fiber with left-handed material core and right-handed material cladding under weak guidance were discussed. Some dispersion equations for TE (TM) mode, EH modes and HE modes were obtained. According to these equations, some curves for different surface modes and oscillating guided modes were plotted. These dispersion equations and curves are compared with each other. Many novel characteristics of surface modes for LHM fiber were obtained.