Single tetragonal La1.5Sr0.5CoO4 ceramics with the space group of I 4/mmm (139) were prepared by a solid-state reaction process, and dielectric characteristics were investigated on a broad frequency and temperature range. There was one obvious dielectric relaxation around room temperature plus a low temperature upturn on the curve of temperature dependence of dielectric properties for La1.5Sr0.5CoO4 ceramics. This dielectric relaxation was a thermal-activated process. It should be attributed to the mixed-valence structure (Co2+/Co3+) since its activation energy was similar to that of small polaronic hopping process. After annealing the sample in O-2 atmosphere, dielectric constants and ac conductivities of La1.5Sr0.5CoO4 ceramics increased and decreased after annealing the sample in N-2 atmosphere. This abnormal phenomenon should be attributed to the variation of concentration for holes (Co3+).