Using 3,4,9,10-perylene tetracarboxylic acid as a bridge to connect mono(6-ethanediamine-6-deoxy)-β-cyclodextrin (NH2-β-CD) to the surface of graphene, noncovalently functionalized graphene nanosheets (CD-PTCA-GNs) are synthesized for the first time. The as-prepared CD-PTCA-GNs were characterized by Fourier transform infrared spectroscopy, thermogravimetric analysis, atomic force microscopy, and electrochemical methods. The electrocatalytic activities toward several persistent organic pollutants (POPs) at the glassy carbon (GC) electrode modified with CD-PTCA-GNs were investigated, all of which show a remarkable increase in electrochemical performance relative to the bare GC and GNs/GC electrodes. 1-aminonaphthalene (1-NA) was used as the representative analyte to demonstrate the sensing performance of the CD-PTCA-GNs. The results show that the linear response range of 1-NA is 10–550 nM with the detection limit of 1.0 nM (S/N=3), thus implying that the CD-PTCA-GNs organic–inorganic nanohybrids will have promising applications in POPs analysis and as sensors.