Selective oxidation of 5-hydroxymethylfurfural (HMF) to 2,5-furandicarboxylic acid (FDCA) is a key reaction in biopolymer production. A non-noble metal catalyst and mild reaction conditions are highlighted in this work. Co-Cu nanoparticles supported on activated carbon (Co-Cu/AC) were introduced in the liquid-phase oxidation of HMF. The catalysts were prepared via a co-impregnation method, followed by reduction with hydrazine. The presence of the Cu promoter resulted in dispersion of the metal particles. The good distribution and small crystal size of Co3O4 significantly increased the active surface area and enhanced the catalytic activity. In addition, the presence of CuO synergized with the oxidation ability of the Co catalyst to increase the FDCA yield. The catalytic activity at different reaction temperatures, reaction times, catalyst loadings, and Co:Cu ratios revealed that the highest selectivity for FDCA (92%) was achieved using the 4Co-Cu/AC catalyst. According to the proposed reaction mechanism, the redox reaction between Cu2+/Cu+ and Co3+/Co4+, together with H2O2 as the oxidant, promotes the complete oxidation of HMF to FDCA.