A positive-electrode material for a lithium secondary battery which includes a lithium oxide compound or a complex oxide as reactive substance. The material also includes at least one type of carbon material, and optionally a binder. A first type of carbon material is provided as a coating on the reactive substance particles surface. A second type of carbon material is carbon black. And a third type of carbon material is a fibrous carbon material a mixture of at least two types of fibrous carbon material different in fiber diameter and/or fiber length. Also, a method for preparing the material as well as lithium secondary batteries including the material.