We have carried out the electrical conductivity and NMR measurements and investigated the characteristic features of the electrical conductivity in a paraelastic phase of Tl2SeO4, It was found from electrical conductivity measurement that the activation energy in the paraelastic phase (above T-c (=661 K)) is 0.98 eV We also found that Tl-205-NMR line width drastically decreases above T-c and becomes approximately 0.5 Gauss. This result indicates that in the paraelastic phase the mobile Tl ions exist. Moreover this result is consistent with the existence of the anomalously large hopping motion of Tl ions observed in X-ray diffraction measurement. Furthermore the activation energy estimated from the motional narrowing of Tl-205-NMR absorption line is 0.92 eV and is in agreement with that obtained from the conductivity measurement. From these results, it is deduced that the mobile TI ions play an important role in the appearance of electrical conductivity in the paraelastic phase. (c) 2006 Elsevier B.V. All rights reserved.