In this paper we propose an efficient scheme to continuously generate two-mode two-photon bundles by using a three-level atomic system, in which two correlated channels are created for the bundle emission in different modes. It is shown that the antibunching effect not only happens between the same modes but also between two different modes. While the former is due to the dominance of cavity decay over atomic decay, the latter is based on the atomic coherence between the two final states of bundle emission. The antibunched two-mode two-photon bundles are achievable in a wide range of parameter...