Thebandgappropertiesofone-dimensionalphotoniccrystalswithadefectlayerofnegativerefractiveindexmaterialsarestudied.Thedefectmodewidthisbiggerthanthatofconventionalone-dimensionalphotoniccrystalswithadefectlayerofpositiverefractiveindexmaterials.Thedefectmodeoftheformerisdifferentfromthatofthelatter,shiftstowardsthedirectionofhighfrequency(shortwavelength),andhasabiggershiftingvelocity.Furthermoretheeffectsonthetransmissionpropertiesoftheformerphotoniccrystalscausedbychangeinthepositionofthedefectlayerofnegativerefractiveindexareinvestigated.Finallytheopticalenhancementoftheformerphotoniccrystalsisalsoinvestigated.