A rubber composition having excellent adhesion to steel cords comprising:(a) 100 parts by weight of at least one rubber selected from the group consisting of natural rubber, synthetic rubber and a blend thereof;(b) from about 0.01 to 1 part by weight of elemental cobalt contained in at least one cobalt oxyketone complex represented by formulae (I) or (II): ##STR1## wherein X.sub.1 -X.sub.4 and Y.sub.1 -Y.sub.10 are as defined in the specification; and(c) from about 0.2 to 10 parts by weight of a bismaleimide compound represented by formula (III): ##STR2## wherein Z represents a hydrocarbon group containing 2 to 10 carbon atoms. The rubber composition has excellent adhesion to steel cord, excellent thermoresistability, and is suitable for use in tire, belt, hose and vibration insulating rubber.