A rubber composition for a tire rim cushion or rubber finishing contains a diene rubber and a filler containing a carbon black. The diene rubber contains a natural rubber and/or an isoprene rubber, and a modified polymer that is obtained by reacting a nitrone compound with a double bond of a conjugated diene polymer. The content of the natural rubber and/or the isoprene rubber in the diene rubber is from 30 to 60 mass %, the content of the modified polymer in the diene rubber is from 8 to 70 mass %, the content of the filler is from 60 to 90 parts by mass per 100 parts by mass of the diene rubber, and the nitrogen adsorption specific surface area of the carbon black is from 60 to 150 m2/g. Such rubber composition has excellent low heat build-up and ozone resistance when formed into a tire.