A method for producing a cathode active material used for a lithium secondary battery, comprising the steps of: mixing lithium carbonate with a compound containing a metal element other than Li in the following formula; and firing a precursor thus obtained via the mixing step thereby to obtain a lithium composite compound represented by the following formula, wherein the firing step includes at least a heat treating substep of performing heat treatment of the precursor while rotating the precursor in a furnace tube of a firing furnace; the furnace tube includes a first gas feeding system that injects an oxidative gas toward an inner circumferential surface of the furnace tube, and a second gas feeding system that makes an oxidative gas flow toward an axis direction of the furnace tube; and the heat treating substep includes: spraying the oxidative gas by the first gas feeding system to the precursor rotating and flowing from an upstream side to a downstream side in the furnace tube; and exhausting a carbon dioxide gas thus generated from the precursor by a flow of the oxidative gas operated via the second gas feeding system to perform the heat treatment, Li 1+a M1O 2+α ----- Formula (where in the formula, M1 is a metal element other than Li and includes at least Ni, a content of the nickel per M1 is more than 70 atom%, and "a" and "α" are the numerals satisfying the following conditions: -0.1 < a < 0.2, -0.2 < α < 0.2). mixing lithium carbonate with a compound containing a metal element other than Li in the following formula; and firing a precursor thus obtained via the mixing step thereby to obtain a lithium composite compound represented by the following formula, wherein the firing step includes at least a heat treating substep of performing heat treatment of the precursor while rotating the precursor in a furnace tube of a firing furnace; the furnace tube includes a first gas feeding system that injects an oxidative gas toward an inner circumferential surface of the furnace tube, and a second gas feeding system that makes an oxidative gas flow toward an axis direction of the furnace tube; and the heat treating substep includes: spraying the oxidative gas by the first gas feeding system to the precursor rotating and flowing from an upstream side to a downstream side in the furnace tube; and exhausting a carbon dioxide gas thus generated from the precursor by a flow of the oxidative gas operated via the second gas feeding system to perform the heat treatment, Li 1+a M1O 2+α ----- Formula (where in the formula, M1 is a metal element other than Li and includes at least Ni, a content of the nickel per M1 is more than 70 atom%, and "a" and "α" are the numerals satisfying the following conditions: -0.1 < a < 0.2, -0.2 < α < 0.2). spraying the oxidative gas by the first gas feeding system to the precursor rotating and flowing from an upstream side to a downstream side in the furnace tube; and exhausting a carbon dioxide gas thus generated from the precursor by a flow of the oxidative gas operated via the second gas feeding system to perform the heat treatment, Li 1+a M1O 2+α ----- Formula (where in the formula, M1 is a metal element other than Li and includes at least Ni, a content of the nickel per M1 is more than 70 atom%, and "a" and "α" are the numerals satisfying the following conditions: -0.1 < a < 0.2, -0.2 < α < 0.2).