Abstract: Using seismological methods, Song and Paul［1］ demonstrated that the rotation of the inner core is faster than the daily rotat ion of the mantle and cr ust. This discovery revealed a noticeable phenomenon that the earth's rotatin g rate is getting slow and the inner core' s rotation is faster than that of the crust and the mantle. They are correlative phenomena of the same dynamic backgr ound. We suggest that the phenomenon is the result of the different tidal fricti on primarily from the moon and the sun. 　　Tidal function might play a very important role in crust evolution, but the succ essful research in the filed is very little till now［8］. Applying the l aw of conser vation of energy can do quantitative analysis. The losing kinetic energy of the crust and the mantle in its long-range slowing rotating may be balanced by the share of dissipated tidal energy in the earth. When calculating the loss of the kinetic energy in the earth, we introduce the prevalent PREM model and quote the parameters h（depth）and ρ (density). From rotary energy (E) formul a E=(1)/(2)Iω2t, where ωt is rotary angular velocity at t moment, I is rotary inertia，　we get ΔE exp ression: ΔE≈Iω0Ωt Where ΔE is loose d rotary energy in t time, ω0 is the beginnin g (t=0) angular velocity, Ω is rotary angular acceleration. Let the total mass of the mantle and crust be 4.10×1024kg, calculating that I≈1. 13×1037kg*m2 (see Table 1), we can see that ΔE≈4.53×1011J ,　when t=1 second. 　　Lambeck (1980) thought that dissipated tidal energy in the total earth equals 4.0×1012J*s-1 is suitable. If the slowing of the earth's rotatio n is mainly gi ven by tidal friction of earth tidal and ocean tidal, let t=1second,　then ΔE is 11 percent of the total dissipated tidal energy in the Earth. The dis sipated tida l energy in the solid inner core is very small. The tidal friction effect is dif ferential from the earth's surface to the core. Because the liquid outer core ca n partly absorb or prevent the tidal function reaching the inner core, the inner core is less influenced by tidal friction.　So, the inner core spinning velocit y is the fastest. In the same way, because the elastic asthenosphere below the l ithosphere can also do the same function as the outer core does, the main mantle sphere (main body of the mantle except the asthenosphere) spins faster than the lithosphere does. So, we can draw a differential rotation model of the three s pheres in the earth: rotation rate of the lithosphere ＜that of main mantle sphe re ＜that of the inner core. The model system is the largest one of layer-slip, plate's drift and magnetic field formation may be of the same background of geo dynamics.