Hydrogen sulfide (H2S) has emerged as an important indicator in the spoilage process of meat. In this study, a mimetic enzyme based on Cu2+-modified boron nitride nanosheets-supported gold nanoparticles (AuNPs/Cu2+-BNNS) was synthesized, which can be used to catalyze the oxidation of 3,3′,5,5′-tetramethylbenzidine (TMB). The H2S gas can inhibit the activity of AuNPs/Cu2+-BNNS toward catalytic oxidation of TMB. Meanwhile, the usage of headspace method could avoid most interferences in the rotten sample. Various concentrations of TMB+ could change the aspect ratio of the gold nanoroads (AuNRs), which results in vivid color changing and UV–vis spectra shifting. The sensor had a good linear relationship with H2S concentration ranging from 10.0 to 90.0 μmol/L, and the detection limit is 7.8 μmol/L. The AuNPs/Cu2+-BNNS sensors were successfully applied to detect H2S produced by meat spoilage with satisfying results.