A rubber composition containing a specifically limited imidazole compound or imidazoline compound, or benzimidazole or its specifically limited derivative has a large tan .delta. at high temperature range, and a tire having a tread using such rubber composition is prevented from being lowered in the value of tan .delta. due to the temperature rising during the running and has an improved grip performance during the high speed running. The use of Bronsted acid in combination with the imidazole, imidazoline or benzimidazole can obviate the drawback of poor scorch resistance of a rubber composition containing the imidazole, imidazoline or benzimidazole alone, and the resulting rubber composition has a very large tan .delta. at high temperature range, and a tire having a tread using the rubber composition has a remarkably improved grip performance during the high speed running.