A core-cladding waveguide structure of the Lithium niobate single crystal fiber with parabolic refractive index profile is achieved by a Mg-ion indiffusion process. The propagstion loss of the cladded crystal fiber is measured, and its loss coefficient is about 14 dB/cm lower than that of the uncladded crystal fiber.The output optical beam patterns of the cladded and uncladded crystal fibers are observed.It is found that three ridges of the cladded crystal fiber core have disappered gtadually in the Mg-ion indiffusion process.