A quaternary Cu2ZnSnS4 compound absorber layers have attracted recently considerable interest as thin film solar cells due to their low cost and low-toxic and abundant elements entering them [1]. It is strongly believed that these materials are alternative of the well-known but more expensive CuIn1−xGaxSe2 thin film solar cell absorber materials, exhibiting at present high conversion efficiency ~ 20 % [2]. Thin film solar cells of Cu2ZnSnS4 with efficiency exceeding 9 % have been already fabricated [3]. Cu2ZnSnS4 is also interesting as a wide-gap p-type thermoelectric material [4], as well as a photoelectrode for H2 evolution from water [5]. In this work are presented investigations of the resistivity of p-Cu2ZnSnS4 single crystals and detailed analysis of the low-temperature resistivity data. The aim of the work is to study the hopping conductivity of the compound and to obtain microscopic properties of the localized carriers, as well as some important macroscopic parameters of p-Cu2ZnSnS4. Another purpose is determination of some significant details of the acceptor band, which is possible in the variablerange hopping conduction regime [6]. Single crystals of Cu2ZnSnS4 were grown by chemical vapor transport using iodine as a transport agent. The grown process was done in evacuated quartz horizontal ampoule from the stoichiometric melt of precursors Cu, Zn, Sn an S of high purity. The evaporation temperature was kept at 850 o C, the grown temperature was 800 o C and the concentration of iodine was 5 mg/cm3. The energy dispersive X-ray microanalysis (EDX) was used to analyze the degree of the stoichiometry of the investigated crystals, yielding a slight excess of Sn and S, the composition ratios being Cu/(Zn + Sn) ≈ 0.98, Zn/Sn ≈ 0.86, S/metals ≈ 1.045. All crystals exhibited p-type conductivity. The difference in composition ratio of samples studied is about 3 % corresponding to the accuracy of our EDX measurements. The resistivity ρ (T) was measured using the van der Pauw method in the temperature interval of 10 − 300 K. The contacts were made by silver paste and the results do not depend on surface treatment. Below ~ 200 K ρ (T) exhibits an activated character, obeying between ~ 130 − 150 K and ~ 30 − 70 K the Mott variable-range hopping conduction law. Analysis of the experimental data yields the values of the relative acceptor concentration, N/Nc ~ 0.72 − 0.84, where Nc ≈ 2.2×1018 cm−3 is the critical concentration of the metal-insulator transition, and those of a/aB ~ 3.5 − 6.4, where a is the localization radius and aB ≈ 19 Å is the Bohr radius, respectively. Width of the acceptor band, W ~ 11 − 22 meV, centered at the energy EB ≈ 22 meV above the top of the valence band, is obtained implying a high degree of the microscopic lattice disorder in the investigated p-Cu2ZnSnS4 samples. The values of the density of localized states, g ~ (4 − 9)×1016 cm−3 meV−1, are estimated, as well. Financial supports from STCU # 5402 and IRSES PVICOKEST – 269167 projects are acknowledged. [1] J. J. Scragg, P. J. Dale, L. M. Peter, G. Zoppi, I. Forbes, Phys. Stat. Sol. (B) 245 (2008) 1772. [2] P. Jackson, D. Hariskos, E. Lotter, S. Paetel, R. Wuerz, R. Menner, W. Wischmann, M. Powalla, Prog. Photovoltaics: Res. Appl. 19 (2011) 894. [3] T. K. Todorov, K. B. Reuter, D. B. Mitzi, Adv. Mater. 22 (2010) E156. [4] Liu Min-Ling, Huang Fu-Qiang, Chen Li-Dong, Chen I-Wei, Appl. Phys. Lett. 94 (2009) 202103. [5] I. Tsuji, Y. Shimodaira, H. Kato, H. Kobayashi, A. Kudo, Chem. Mater. 22 (2010) 1402. [6] B. I. Shklovskii, A. L. Efros, Electronic Properties of Doped Semiconductors, Springer, Berlin, 1984