Copper foam with dendritic copper nanostructure was synthesized by an electrodeposition process using hydrogen bubbles as dynamic templates. To modify the morphology of the copper nanostructure in the foam walls, (NH4)2SO4 and BTA (benzotriazole) were introduced into the electrolytic bath as chemical additives, and their influences on the morphologies and the structural characteristics of copper deposits were examined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The mechanical strength and stiffness of the copper foam were evaluated by the compression test. The corncob-like deposits of the copper foam were changed to needle-like nanodendrites by the addition of (NH4)2SO4, which significantly improved the mechanical strength and stiffness due to the self-supporting effects of the tightly interlocked needle-like nanodendrites. In contrast, the copper foam prepared from the solution with (NH4)2SO4 and BTA shows high ductility but low mechanical strength due to the formation to grape-like copper deposits. Both the copper foams exhibited higher mechanical properties than the one with corncob-like deposits formed in the additive-free solution. The reaction mechanism of (NH4)2SO4 and BTA on the nanostructure of the copper foam at high cathodic current density was clarified by analyzing the effects of the additives on the copper deposition reaction and hydrogen gas evolution reaction, respectively.