NOVELTY - The porous carbonaceous composite material comprises: an oxygen functionalized carbon nanotube (CNT); a modified carbonaceous material doped with a heterogeneous element, where a ratio of the number of surface oxygen atoms to the number of surface carbon atoms ranges 2-15 atom %; a core including the oxygen functionalized CNT; and a coating layer arranged to cover a portion of the core, where the coating layer comprises the modified carbonaceous material. The core comprises oxygen functionalized CNTs, and pores existing between the oxygen functionalized CNTs.    USE - The porous carbonaceous composite material is useful in a positive electrode of a lithium air battery (all claimed) such as lithium primary battery and lithium secondary battery, that is used in an electric vehicle.    ADVANTAGE - The porous carbonaceous composite material reduces the polarization during charging and discharging of the lithium air battery thus enhancing energy efficiency of the lithium air battery.    DETAILED DESCRIPTION - The porous carbonaceous composite material comprises: an oxygen functionalized carbon nanotube (CNT); a modified carbonaceous material doped with a heterogeneous element, where a ratio of the number of surface oxygen atoms to the number of surface carbon atoms ranges 2-15 atom %; a core including the oxygen functionalized CNT; and a coating layer arranged to cover a portion of the core, where the coating layer comprises the modified carbonaceous material. The core comprises oxygen functionalized CNTs, and pores existing between the oxygen functionalized CNTs. An average diameter of the carbon nanoparticle is 2-900 nm. The ratio of a number of the heterogeneous elements doped into the coating layer to a total number of atoms contained in the coating layer is less than or equal to 30 atm.%. The oxygen functionalized CNT is a single-walled oxygen functionalized CNT, a double-walled oxygen functionalized CNT, a multi-walled oxygen functionalized CNT, a semiconducting oxygen functionalized CNT and/or a metallic oxygen functionalized CNT. An average pore size of the porous carbonaceous composite material as a value measured by a Brunauer-Emmett-Teller (BET) method ranges 1-200 nm. A specific surface area of the porous carbonaceous composite material as a value measured by the BET method ranges 100-900 m2/g. INDEPENDENT CLAIMS are included for:    (1) a positive electrode;    (2) a lithium air battery; and    (3) a method of preparing a porous carbonaceous composite material.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic sectional view of a lithium air battery.    First current collector (12)    Negative electrode (13)    Second current collector (14)    Positive electrode (15)    Separator. (16)