MFs with three zero-dispersion wavelengths are studied and designed by multi-pole method. Phase mismatch of this kind of MFs with d/Λ=0.40, Λ=1.8μm is studied when pump locates at all three zero-dispersion wavelengths and the wavelengths of some commonly used lasers. Numerical results show that broadband phase match can be achieved when the pump varies from the normal dispersion regime around the first zero-dispersion wavelength to the last zero-dispersion wavelength and two sets of phase matched wavelengths exist when the wavelengths of pump are in the anomalous dispersion regime between the first two zero-dispersion wavelengths. Then, a little air-hole is added in the fiber core and the dispersion characteristics of the new MFs are investigated for MFs with four zero-dispersion wavelengths. The phase matching topology of this kind of MFs with d/Λ=0.80, Λ=2.2μm, d0=0.636μm is analyzed when the pump is in the anomalous dispersion regime, zero-dispersion wavelength and normal dispersion regime of the fiber. Two sets of phase matched wavelengths can also be found when the MF is pumped in the anomalous dispersion regime between two neighboring zero-dispersion wavelengths. Interestingly, when the MF is pumped in the normal dispersion regime between the second and third zero-dispersion wavelength, three phase matched wavelengths sets appear. For MFs with multiple zero-dispersion wavelengths mentioned above, in entire phase matching band, there always exists one Stokes wave whose wavelength is longer than the longest zero-dispersion wavelength of the fiber, which will provide more possibilities for frequency conversion in mid-infrared band.