We propose how to achieve strong photon antibunching effect in a cavity-QED system coupled with two Rydberg-Rydberg interaction atoms. Via calculating the equal time second order correlation function g(2)(0), we find that the unconventional photon blockade and the conventional photon blockade appear in the atom-driven scheme, and they are both significantly affected by the Rydberg-Rydberg interaction. We also find that under appropriate parameters, the photon antibunching and the mean photon number can be significantly enhanced by combining the conventional photon blockade and the unconventional photon blockade. In the cavity-driven scheme, the existence of the Rydberg-Rydberg interaction severely destroys the photon antibunching under the unconventional photon blockade mechanism. These results will help to guide the implementation of the single photon emitter in the Rydberg atoms-cavity system.
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