Nanocomposite solid electrolytes were prepared by impregnation of LiClO4 into pores of the metal-organic framework Cr3[C6H4(COO)2]3F (MIL-101(Cr)), and their conductivity was investigated. At temperatures 25–150 °C and relative humidity of 50%, the composites easily absorb water with formation liquid phase in the pores and have conductivity values typical for water solutions. Conductivity decreases with diminishing the humidity; however, complete dehydration may be achieved only after prolonged heating in vacuum at 180 °C. The concentration dependence of conductivity of dehydrated samples goes through the maximum at nearly 6 mol% of MIL-101(Cr) and reaches 3 × 10−3 S/cm at 160 °C; the activation energy decreases in the nanocomposites. Using the volt-amperometric technique on the sample with two nickel electrodes, the electrochemical decomposition voltage value was found to be nearly 3.5 V at 160 °C. It suggests that the ionic conductivity is caused by lithium cations rather than protons or electrons.