The electronic density of states, spin-splittings and atomic magnetic moment of RE-TM compound SmCo55 have been studied by spin-polarized MS-Xα method. The results show that a few of electrons are transferred to Sm(5d00) o rbital because of orbital hybridization between Sm and Co atoms in the compound. The exchange interactions between 3d and 5d electrons lead to the magnetic coupling betwee n Sm and Co, and therefore, result in the long-range ferromagnetic order inside the compound SmCo55 There are some negative exchange couplings occ urring at six levels, which make the Curie temperature of SmCo55 decrease disti nctly, com pared with pure Co. The spin moment and orbital moment of 2c and 3g site s have been also studied in this paper. We found that the spin moment, orbital m oment and its quenched part of Co(2c) are greater than that of Co(3g).Th erefore, the strength of L-S coupling of the former is a little greater tha n that of the latter, which implies the contribution to magneto-anisotropy of 2c site is greater than that of 3g site. But the unquenched orbital mome nt in 2c site is slightly smaller than that in 3g site. So, the differen ce of contribution to the anisotropy between the two Co-sites is not very disti nct. Considering the localization of 4f electrons and the few 5d electrons, the magnetic moment of Sm atom will be 129μBB in SmCo55, wh ich is in agreem ent with the experiments of Sm3+3+ ion-moment (132—163μBB) and the Sm atom-moment (174μBB) in metal.