When the hexagonal structure parameters are changed, the dispersion coefficient and nonlinear coefficient with two zero-dispersion of photonic crystal fiber as a function of wavelength is investigated from the near infrared wavelength to the range of communication band by multipole method. We compare photonic crystal fiber of hexagonal structure with that of octagonal structure, both of which have the same structural parameters. The two zero-dispersion wavelengths of photonic crystal fiber with hexagonal structure are much flatter and the nonlinear coefficient of photonic crystal fiber with hexagonal structure is significantly increased, so the photonic crystal fiber with hexagonal structure is more accessible to flattened high nonlinearity and two zero-dispersion wavelengths. It is shown from numerical results that it is possible to design photonic crystal fiber of hexagonal structure with two zero-dispersion and high nonlinear coefficient around 800 nm.