Ocean drilling has revealed that, although a minor mineral phase, native Cu ubiquitously occurs in the oceanic crust. Cu isotope systematics for native Cu from a set of occurrences from volcanic basement and sediment cover of the oceanic crust drilled at several sites in the Pacific, Atlantic and Indian oceans constrains the sources of Cu and processes that produced Cu0. We propose that both hydrothermally-released Cu and seawater were the sources of Cu at these sites. Phase stability diagrams suggest that Cu0 precipitation is favored only under strictly anoxic, but not sulfidic conditions at circum-neutral pH even at low temperature. In the basaltic basement, dissolution of primary igneous and potentially hydrothermal Cu-sulfides leads to Cu0 precipitation along veins. The restricted Cu-isotope variations (δ65Cu = 0.02 – 0.19‰) similar to host volcanic rocks suggest that Cu0 precipitation occurred under conditions where Cu+-species were dominant, precluding Cu redox fractionation. In contrast, the Cu-isotope variations observed in the Cu0 from sedimentary layers yield larger Cu-isotope fractionation (δ65Cu = 0.41 – 0.95‰) suggesting that Cu0 precipitation involved redox processes during the diagenesis, with potentially seawater as the primary Cu source. We interpret that native Cu precipitation in the basaltic basement is a result of low temperature (20°-65 °C) hydrothermal processes under anoxic, but not H2S-rich conditions. Consistent with positive δ65Cu signatures, the sediment cover receives major Cu contribution from hydrogenous (i.e., seawater) sources, although hydrothermal contribution from plume fallout cannot be entirely discarded. In this case, disseminated hydrogenous and/or hydrothermal Cu might be diagenetically remobilized and reprecipitated as Cu0 in reducing microenvironment.