(Pt/Co)n/FeMn multilayers with perpendicular anisotropy (PA) were prepared by magnetron sputtering with Pt as the buffer layer and the capping layer. The dependence of perpendicular exchange bias (PEB), Hex, on the thickness of the FeMn antiferromagnet (AFM) layer is similar to that of in-plane exchange bias. The value of Hex for the (Pt/Co)3/FeMn multilayer reaches 22.3 kA/m. A thin Pt spacer was inserted between the Co/FeMn interface to enhance PEB. The PEB reaches the largest at 39.8 kA/m when the thickness of the Pt spacer is 0.4 nm.