Abstract: There exist relationship between the Earth’s inner core and the Earth’s rotation.Because of the inner core of the Earth,there will have two new nutation modes related to the Earth’s rotation,i.e.a prograde free core nutation (PFCN) mode and a inner core wobble (ICW) mode.Based on the inner core nutation theory of the Earth by Mathew’s et al the applications of normaliged nutation amplitude of Mathew’s type and Whar’s one are discussed,By the PREM Earth’s model,the influence of the inner core to the vibration rangeof nutation is checked,the main solution is that the inner core has effects to the main nutation terms in 0.1 mas,which is coincide with recent observation precision.