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An approach to the enhancement of Cherenkov radiation source driven by two electron beams (TEBs) is presented in this paper. The Cherenkov radiation source is composed of a cylindrical grating, and TEBs with a velocity separation are concentric and separated. By a field matched method, the dispersion equation is derived with a linearized fluid theory and solved by numerical calculation. The numerical results show that a considerable enhancement of growth rate is realized at an optimized voltage ratio due to two stream instability. Moreover, with a help of 2-D particle-in-cell simulations, the improvement of output power induced by the two stream instability is demonstrated, and the decreased of output power is observed as the increased distance of two electron beams.