In this paper, we report the observation of exchange bias in (Pt/Co)n /FeMn multilayer with perpendicular magnetic anisotropy. The samples were deposi ted on glass substrates by magnetron sputtering and capped with 2nm thick Pt lay er. Our results show that the relation between perpendicular exchange bias Hex of (Pt/Co)n/FeMn multilayers and the thickness of antiferro magnetic layer is similar to that in the case of in-plane exchange bias. He x is inversely proportional to the number of bilayer repeats. In the case of (Pt/Co)3/FeMn multilayers, perpendicular exchange bias Hex reachs 22.3kA/m. With insertion of 0.4nm Pt layer between Co layer and FeMn layer, Hex can reach 39.8kA/m.