PROBLEM TO BE SOLVED: To provide a method of producing a composite material of nano particles of lithium titanate and conductive carbons, the composite material not substantially containing titanium oxide that is prone to be by-produced in lithium-titanate production.SOLUTION: The composite material not substantially containing titanium oxide can be produced through the steps of: (a) introducing a reaction liquid containing a lithium source, a titanium source and conductive carbon powder into a reactor that can be swirled; (b) carrying a lithium-titanate precursor on the conductive carbon powder by swirling the reactor and applying a shear stress and a centrifugal force to the reaction liquid; and (c) inverting the lithium-titanate precursor into nano particles of spinel type lithium titanate on the conductive carbon powder by performing primary calcination of the conductive carbon powder carrying the obtained lithium-titanate precursor at a temperature of 200 to 500°C and then performing secondary calcinati
