Neutron diffraction measurements on the $La_0.5Sr_{0.5-x}Ba_xCoO_3$(x=0, 0.01, .15, 0.25) were carried out over a range of temperature from 50K to room temperature. It was found that the magnetic transition occurred between 50K and 250K. Based on the X-ray and neutron diffraction results, the space group of present oxide system could be determined to be R $\bar{3}c$. By refining the parameters used in Rietveld method, it was demonstrated in the neutron diffraction that the rhombohedral distortion was decreased with the increased Ba contents. The magnetic structure determination of the x=0, 0.15 compounds at 50K was accomplished by using low temperature neutron diffraction. Using the magnetic subgroup C2/c, magnetic structures of compounds were investigated.
