The group delay and group velocity dispersion (GVD) of the fundamental mode was proposed by derivative action on the characteristic equation directly and the influence of different index contribution of doubly clad single-mode fibers on propagation constant, group delay, group velocity dispersion and the zero dispersion wavelength were studied. The research results indicate that the optical parameters, i.e., relative index of inner clad and outer clad (R) and relative index of the core and outer clad (P), have distinct impact on propagation constant, group delay, group velocity dispersion and zero dispersion wavelength and the rules of impact vary with the parameters. These rules provide theoretical basis for designing doubly clad single-mode fibers catering for different dispersion.