The applieation of the ab-initio LMTO-ASA method to B1 structure crystal is studied in this paper. The important function of the empty atomsphere in the calculation of static properties such as equilibrium lattic constant, bulk modulus and cohesiv energy, and the band structure on Bl MgO crystal are emphatically investigated. A simple LMTO method which is as accurate as the ab-initio pseudopotential method has been adopted. The calculated results of the lattic constant a0 ,bulk moduius B0 and cohesive energy Ec of Bl MgO are 4.21? , 1.58 Mbar and 5. 73eV/atom, respectively, which are very close to experimantal data and those obtained by more complicated ab-initio band calculating methods. The band structure calculated by our method is in good agreement with that by ab-initio pseudopotential method. The results indieate that LMTO-ASA method in which empty atom-spheres is added and L?wdin principle is introduced to raise calculation efficiency is suitable to the study of band structure and static property of Bl structure crystal.