Nano crystalline cobalt substituted lithium ferrites having chemical formula [Li 0.5Fe0.5]1-x Cox Fe2O4 (where x=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) have been prepared by the citrate gel auto combustion method at low temperature (180 o C). The prepared samples were sintered at 500 o C for 4 hours. Single phase of these samples were confirmed by x-ray powder diffraction technique and found that lattice parameter increases with increasing with the Cobalt substituted concentration, and the values of crystallite size, x-ray density, bulk density and porosity of the prepared samples were calculated from the XRD analysis. The dc electrical resistivities of the prepared Li-Co ferrites were studied by using the two probe method in the temperature range of 473-873 K (200-600 o C). A plot of log (?T) vs inverse of temperature yields a almost straight line which reveals the semiconducting behavior of prepared ferrite samples. The dielectric properties namely dielectric constant (ε'), dielectric loss tangent (tan δ) of these Li-Co nano crystalline ferrites have been studied using an LCR meter from the room temperature to 700 K at various selected frequencies up to 5 MHz. The dielectric constant (ε') of all prepared samples was increased with increasing in temperature. These results have been explained on the basis of Koop’s theory, concentration of Fe +2 and Fe +3 ions on the octahedral site and hoping frequency of charge carriers (electrons) between Fe +2 and Fe +3  ions.