The photoluminescence of calixarene crystals has been studied as functions of temperature, time, and concentration. The vibronic bands shift to longer wavelength and become significantly sharper as temperature decreases. The experimental results r eveal that the structural transformation occur during the annealing process. Time-resolved spectra of calixarene at 12 K are monitored. Spectral features, which demonstrate characteristic of energy transfer processes, are not observed. The depopulation of excited state density is mainly controlled by unimolecular decay process dominating other decay processes. The lifetime was found to be 2.6 $pm$ 0.1 ns. For the case of calixarene mixed with naphthalene, the fluorescence spectrum shows that the band centered at 340 nm lies 2840 $cm^{-1}$ below the relatively broad 310 nm band found for calixarene crystals. The spectra also exhibit that the emission intensity increases with increasing calixarene concentration. The results are evident that the calixarene emission is quenched by the naphthalene. Phosphorescence of calixarene mixed with naphthalene crystals is observed to determine whether the emission is due to naphthalene. The phosphorescence peaks were compared with the ground-state vibrational frequencies of naphthalene and found to be in good agreement. The results indicate that inter-molecular energy transfer occurs between calixarene and naphthalene.