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The advantages of the MgB2 compound are the high Tc value (39 K) and lower material cost than other superconducting metallic compounds. In addition, MgB2 wire has a shorter decay time for induced radioactive properties than Nb-based superconductors. However, the Jc value of MgB2 wire is poor compared with Nb-based superconductors, and further improvement of Jc is required if the compound is to be used in a future nuclear fusion reactor. In order to improve Jc, we investigated Cu addition using the Mg2Cu compound in MgB2/Fe-sheathed wires through the powder-in-tube (PIT) process. Tc values of Cu addition samples were higher than those of non-Cu addition samples and they were improved with increasing Cu addition. We obtained maximum core Jc values over 100 A mm−2 at 4.2 K under 8 T for 1 and 3 at.% Cu addition samples. Moreover, we found that Cu addition was more effective at improving the value of Jc in low and middle magnetic fields than the SiC addition process.