The　vibration　signal　from　the　rotatory　machinery　condition　monitoring　under　time-varying　speed　is　usually　amplitude-modulated　(AM)　and　frequency-modulated　(FM).　It　is　important　to　efficiently　and　accurately　estimate　the　instantaneous　frequency　(IF)　of　the　vibration　signal.　In　this　paper,　a　novel　parameterized　IF　estimation　method　is　proposed.　The　method　employs　a　high-order　polynomial　function　to　approximate　the　nonlinear　IF　and　subsequently　constructs　overdetermined　systems　of　linear　equations　by　calculating　the　Fourier　transform　of　the　derivative　of　the　signal.　The　IF　can　be　estimated　by　using　least　squares　estimation　to　solve　the　equations.　The　proposed　method　has　high　computational　efficiency　because　it　can　obtain　the　estimation　of　IF　over　a　period　of　time　simultaneously;　it　differs　from　traditional　time-frequency　analysis　methods　that　need　to　calculate　the　IF　at　each　point　in　the　time　axis.　It　is　demonstrated　that　the　proposed　method　is　not　only　particularly　powerful　for　the　nonlinear　FM　mono-component　signal　but　also　applicable　to　the　multi-component　signal　constructed　by　multiple　harmonics.　The　numerical　simulation　validates　the　effectiveness　of　the　proposed　method,　and　the　experiment＇s　results　show　that　the　method　is　suitable　for　the　IF　estimation　of　the　vibration　signal　from　the　varying-speed　rotor　system.