Quantum　walks　are　a　kind　of　basic　quantum　computation　model.　Quantum　walks　with　memory(QWM)　are　types　of　modified　quantum　walks　that　record　the　walker＇s　latest　path.　In　this　paper　we　present　QWM-P,　a　kind　of　QWM　whose　evolution　depends　on　the　parity　of　memory.　QWM-P　has　an　identity　coin　shift　function　which　helps　in　analyzing　and　designing　algorithms.　Then　we　discuss　some　properties　of　QWM-P.　We　find　that　the　parity　of　memory　length　affects　the　appearance　of　QWM-P.