In this paper, we have verified that the KLiSO4 single crystal is a Li ionic conductor. It was determined that carriers in KLiSO4 single crystal are interstitial Li ions and Li vacancies by measuring the voltage distribution in the specimen. After turning off the applied dc voltage, the decrease of current follows a negative power law of time in a certain time domain. Correspondingly, the dielectric dispersion which has a negative power relationship with frequency has also been found in a certain frequency domain. The background current, the dc electric conductivity and the apparent dielectric constant of KLiSO4 single crystal exhibit sharp peaks besides jump nearby the transition temperature. These peaks were observed only when the rate of temperature change is low, thus it is shown that the phase transition includes a relaxation process.