Cu/N-C derived from MOF composites were synthesized and characterized by scanning electron microscopy, X-ray diffraction, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and electrochemical impedance spectroscopy, which was modified on the glassy carbon electrode (GCE) to construct a novel electrochemical sensor (Cu/N-C/GCE). Due to the good electrical conductivity and abundant catalytic active sites of Cu/N-C, Cu/N-C/GCE exhibited excellent electrocatalytic performance for catechol (CC) and hydroquinone (HQ) with the oxidation peak potential difference of 112 mV. The proposed sensor could realize the simultaneous detection of CC and HQ successfully. Under optimal conditions, the redox peak currents of both CC and HQ have good linear relationship with their concentrations in the ranges of 0.50-100.00 μM and 0.50-150.00 μM with the detection limits for CC and HQ of 0.12 and 0.09 μM, respectively. At the same time, the sensor exhibits good stability, reproducibility and selectivity in the analysis of practical samples.