We investigated the magnetic property of Co/Ni multi-layers onW(110), using first principles calculation based on density functional theory. We found that one atomic monolayer of Ni (Ni 1ML) and two atomic monolayers of Ni (Ni 2ML) on W(110) exhibited no magnetic moment. These results occur because the minority spin states of Ni atoms are occupied by the electrons transferred from W atoms. These results also agree with the experimental results where the 1ML and 2ML of Ni layers exhibited no magnetic anisotropy. We calculated the magnetic anisotropy energy in each of the three directions, viz., the two surface in-plane directions and one surface out-of-plane direction, in Ni 1ML, Ni 2ML and Co 1ML/Ni 2ML on W(110).We found that the Co surface atoms of Co 1ML/Ni 2ML exhibit surface in-plane magnetic anisotropy. We also estimated the effect of magnetic dipole-dipole interaction on the magnetic anisotropy energy in a Co 1ML/Ni 2ML multi-layer on W(110). We found that the effect is not dominant.