Ac electrical conductivity of LiCrP2O7 compound is been investigated by means of impedance spectroscopy measurements over the frequency and temperature ranges of 40 Hz-7 MHz and 460 to 700 K, respectively. The real and imaginary parts of complex impedance are well fitted to two equivalent circuit models. Besides, the nature of frequency dependence of ac conductivity follows the Jonscher's law, while calculated dc conductivity follows Arrhenius behavior with two different activation energies E-dc(I) = 0.49 eV for T < 550 K and E-dc(II) = 0.91 eV for T > 550 K. Actually, the values of activation energies obtained from the impedance E-a (I and II), dc conductivity E-dc (I and II) and the relaxation time E-tau (I and II) are in good agreement, and hence the transport in the titled compound can be described through a simple hopping mechanism, dominated by the motion of Li+ ions. The temperature dependence of the power s-factor shows a decrease below 550 +/- (5) K with increasing temperature (region I) whereas above 550 +/- (5) K (region II), it increases with increasing temperature. An agreement between the experimental and theoretical results are discussed and it is suggested that the ac conductivity can be explained by the correlated barrier hopping (CBH) and non-overlapping small polaron tunneling model (NSPT) in region I and II, respectively. (C) 2015 Elsevier B.V. All rights reserved.