Cu–Ti alloy is one of precipitation hardening alloys with two types of the precipitates such as β’– and β–Cu₄Ti. These precipitates dissolve in Cu matrix during cold working, lowering the conductivity considerably. To prevent the re–dissolution of them, the stability of them should be improved so that they can be stably present even after severe deformation. We have studied the effect of additional 3d transition metals （TMs） on the stability of the precipitates in Cu–Ti alloy, using the simulations based on density functional theory （DFT）. According to the DFT calculations, each Cr, Mn, Fe, Co and Ni atoms prefers to bind with a Ti atom in Cu matrix. When these 5 elements are doped in β’– and β– Cu₄Ti, respectively, the cohesive energies of two phases decrease, indicating that the precipitates can be stabilized in Cu matrix by the TM doping. Especially, Co atoms can decrease the interfacial energy and increase the most unstable stacking fault energy （USFE） for β–Cu₄Ti. It means that the Co addition can stabilize the precipitates effectively, and the slip activation barrier can increase in Co doped precipitates. Therefore, the addition of Co to the Cu–Ti alloy has a very high possibility of suppressing the re–dissolution of the precipitated phase during cold working if Co atoms are well positioned in the precipitates without making another phase.