Quenching of photoexcited triplet-state anthracene through triplet-triplet (T-T) energy transfer mechanism by a few energy acceptors, azulene, ferrocene, and also anthracene in the ground state, is investigated in a dehydrated Na+ form of zeolite Y (NaY) with a transient absorption spectroscopy utilizing a diffuse reflectance detection technique. It is found that the decay curves of T-T absorption for anthracene follow unconventional kinetics that can be handled by a model based on the continuous time random walk (CTRW) theory. The analysis of the quenching kinetics affords an estimate of the intrazeolite self-diffusion coefficient for the guest aromatic species. Presently, a simplified version of the CTRW treatment is developed which enables us to extract information concerning, the diffusivity only by analyzing the long time tail of triplet decay signals measured by a conventional photomultiplier detection system with limited time resolution. The self-diffusion coefficients thus obtained, ranging from 10(-15) to 10(-16) m(2) s(-1) in NaY at 298 K, are significantly smaller than those observed for benzene (10(-10)-10(-13) m(2) s(-1)). This study demonstrates that the triplet quenching method is a powerful technique for evaluating diffusion coefficients of relatively large organic molecules with small intrazeolite mobility that are hardly measurable by NMR and other traditional techniques.