The　measured　vibration　signals　of　mechanical　equipment　with　defects　are　generally　non-stationary.　Time–frequency　analysis　is　an　effective　tool　in　processing　non-stationary　signals.　However,　the　concentration　of　time–frequency　representation　will　greatly　affect　the　performance　of　feature　extraction.　Thus,　a　more　concentrated　time–frequency　analysis　method　plays　an　important　role　in　mechanical　signal　processing　and　fault　diagnosis.　A　novel　time–frequency　analysis　method,　called　synchrosqueezing　extracting　transform　has　been　proposed　in　this　study.　The　proposed　method　can　not　only　well　extract　the　time-varying　information　of　the　nonstationary　signal　then　achieve　a　better-concentrated　time–frequency　representation,　but　also　have　better　noise　robustness　and　lower　time-consuming　than　the　traditional　time–frequency　analysis　methods.　The　analysis　of　numerical　signals　verified　the　great　performance　of　this　method.　Finally,　synchrosqueezing　extracting　transform　is　used　to　process　the　bearing　vibration　signals　under　variable　speed　conditions.　It　has　been　demonstrated　that　the　proposed　method　achieves　better　results　than　other　state-of-art　time–frequency　analysis　methods.　©　2020　Elsevier　Ltd