An object of the invention is to provide such an additive for a lithium secondary battery that improves the battery capacity and the initial efficiency of the lithium secondary battery.In the invention, a fullerene derivative having a group having a formula weight of 6 or more is used as an additive for a lithium secondary battery. A fullerene derivative having a group having a formula weight of 6 or more is contained in an anode material for a lithium secondary battery, an anode for a lithium secondary battery, and a lithium secondary battery using an anode containing the anode material. The group having a formula weight of 6 or more in the fullerene derivative is preferably one selected from the group consisting of an alkali metal atom, a chalcogen atom, a halogen atom, an aliphatic hydrocarbon group, an aromatic hydrocarbon group, a heterocyclic group, a characteristic group containing oxygen, a characteristic group containing sulfur and a characteristic group containing nitrogen.