Based on the full potential linearized plane wave method of first principle,the calculations of the total energy and the equilibrium lattice constant for the body-centered cubic(bcc)PbS compound have been performed within different exchange-correlation potentials(DECP)on both the generalized gradient approximation(GGA)and the local density approximation(LDA).The effect of DECP on the band structure,the density of states,the partial density of states and the band gap are discussed,respectively.The energy calculation shows that the face-centered cubic structure is found to be the more stable one than that of the bcc structure.In addition,band structure calculations in the bcc structure show a band-gap existence,which agrees well with experimental results of other Pb chalcogenide compound(PbTe).The above result of PbS(bcc)is helpful to the experimental study in the future.