The band gap structure and filter properties in one dimensional photonic crystals with quasiperiods were studied. The transmission spectra were calculated in photonic crystal with quasiperiodic structure arranged alternatingly by ZnS and MgF2 or GaAs and AlAs as the thickness of layers unchanged and the index of refraction changed or the index of refraction unchanged and the thickness of layers changed or the rate of index of refraction changed. The band gap structures were obtained and the application was discussed. Comparing to the optical crystals with periodic structure, the transmission spectra in one dimensional optical crystals with quasiperiods shifted and the band gap width changed