The quenching of 9,10-bis(phenylethynyl)anthracene (BPEA) fluorescence by carbon tetrabromide (CBr4) is investigated in supercritical carbon dioxide as a function of densities. Fluorescence lifetimes of BPEA at different CBr4 concentrations are determined using the time-correlated single photon counting method. While the fluorescence decays adhere closely to single-exponential functions and the CBr4 concentration dependence follows the Stern-Volmer relationship, the quenching of fluorescence lifetime is unusually efficient at near-critical densities. The results are in support of a solute-solute clustering mechanism in which the enhanced bimolecular reactions are attributed to a higher local quencher concentration than the bulk under near-critical solvent conditions.