The optical characteristics of guided modes in a fiber formed by a core with usual refractive index and a negative refractive index cladding are studied. The difference compared with normal fiber is analyzed through the dispersion curves showing less degenerate modes and larger single-mode area. When the cladding refractive index tends to zero, the optical characteristics are different from the former two fibers. A single-mode in the smaller region V is found, when the permittivity or permeability of the cladding is zero. It is quite different from the mode HE11 in a normal fiber, its dispersive curve has an opposite tendency, and there are some areas where no modes could exist.