The chirped Gaussian pulse broadening induced by chromatic dispersion in two kinds of tripleclad single-mode fibers with a depressed index inner cladding was examined in this paper. In view of the impossibility to deduce the expression of chromatic dispersion directly due to the complexity of the characteristic equations, a feasible approach to calculate chromatic dispersion was established, and the influences made by the optical parameters and geometric parameters on the chromatic dispersion and chirped Gaussian pulse broadening were analyzed. The calculated results indicated that the optical parameter, that symbolizes the third clad effect, has a strong impact on chromatic dispersion and pulse broadening, and the degrees of such impact were closely related to the other parameters and operating wavelength. The evolvement processes of a traveling chirped Gaussian pulse in the kinds of triple-clad single-mode fibers with different parameters were also analyzed