In this work, La2-xSrxCoO4 (x = 0.4, 0.5, and 0.6) crystals with the Ruddlesden-Popper K2NiF4-type structure have been grown by the floating zone method. This compound crystallizes in the K2NiF4-type structure with space group 14/mmm. Temperature-dependent dielectric properties of the as-grown crystals were studied over a broad frequency range. The origin of the giant dielectric constant in this system is the mixed-valence structure between Co2+ and Co3+, and the dielectric constant at high frequency is related to the charge ordering structure. The dielectric relaxation shows a thermally-activated behavior. The corresponding activation energy (assigned to small polaronic hopping) can be obtained by Arrhenius fitting. (C) 2014 Elsevier Ltd. All rights reserved.