Currently, the catalytic reduction of nitrobenzene requires more efficient and low-cost catalysts. In this work, a new copper-based metal-organic framework (MOF) was designed by the calcination of Cu–MOF at 700 °C (denoted as Cu@C). The catalyst showed superior catalytic performance toward the reduction of nitrobenzene, using sodium borohydride (NaBH4) as the reducing agent, and the catalyst exhibited high nitrobenzene conversion (100%) and a quick reaction time (8 min). This was one of the highest efficiencies among non-noble metal catalysts reported so far, as general non-noble metal catalysts typically require more than 15 min. This catalyst had excellent acid resistance after etching using sulfuric acid (H2SO4) for 24 h with a nitrobenzene conversion rate that was still more than 90%. In addition, it could be used more than five times and the catalytic properties remained essentially unchanged, without any reactivation treatment. Therefore, this study could offer a new efficient non-noble metal catalyst for the reduction of nitro compounds.