The Hamiltonian of the four-body problem for a lithium atom is expanded in series. The level shift and levelformula of a lithium atom in Rydberg states are achieved by means of the calculation of polarization of the atomic core(including the contribution of dipole, quadrupole and octupole components). We also consider the effect of relativitytheory, the orbital angular momentum L and the spin angular momentum S coupling scheme (LS coupling) and high-order correction of the effective potential to the level shift. The fine structure splitting (N＝5-12, L＝4-9, J＝L±l/2)and level intervals in B ydberg states have been calculated by the above-mentioned formula and compared with recentexperimental data.