The characteristic equation of a doubly cladding fiber with an inner cladding made of negative refractive index material is presented by full vectorial mode method. Its mode distribution, dispersion and time delay are demonstrated. The results indicate that this kind of fiber has some abnormal properties, such as the single mode existing in certain normal frequency. Along with increasing diameter of inner cladding, different propagation constants exist in the same mode and normalized frequency. The diameter of inner cladding has great influence on the dispersion and group time delay. The dispersion can reach -158000 ps/(nm·km) and group time delay can become very large by increasing the diameter of the inner cladding. These results provide theoretical basis for designing novel dispersion compensating fiber and photonic devices.