A double cladding photonic crystal fiber with hexagonal air hole lattice, whose claddings are made by two different sizes of air holes, is designed and the influence of the geometric parameters on its dispersion and low dispersion bandwidth are investigated. The results show that the dispersion, low dispersion bandwidth and the nonlinearity are easily tailored by adjusting the two different sizes of air holes in the cladding as well as the pitch. The near-zero dispersion of (0±1.8) ps·km-1·nm-1 at C and L band can be obtained by optimizing design.