The ceramic varistors SnO2–Co3O4–Nb2O5–Cr2O3 with the addition of CaCO3, SrCO3 or BaCO3 were sintered at temperatures 1250 and 1350°C, then their structures and electrical properties were studied. In all samples, the SnO2 cassiterite phase with a rutile-type structure and the Co2SnO4 phase with a spinel-type structure were observed. All materials exhibited a highly nonlinear dependence of the current density on the electric field with the nonlinearity coefficient 24–50. When alkaline earth metal carbonates were added, the grain size of all samples decreased and the electric field E1 increased. The addition of CaCO3 lead to the decrease of the low-field electrical conductivity of varistors. The lowest low-field conductivities 4·10–13 and 6·10–13 Ω–1 cm–1 were found in the samples with CaCO3 addition baked at 1250 and 1350°C, respectively. The observed effect is due to the increase of the potential barrier height at the SnO2 grain boundaries by 7 and 13%, respectively, and the decrease of the grain size by 26 and 28% compared to SnO2-based varistor ceramics without CaCO3 addition.