Chaos is a fascinating phenomenon of nonlinear dynamical systems, and optical chaos communication has been one of potential frontier techniques to implement secure transmission of information. In this paper a novel high-speed bidirectional dual-channel chaos secure communication system is proposed based on semiconductor ring lasers (SRLs). In this system, the time delay signatures in chaotic output of clockwise (CW) and counterclockwise (CCW) patterns from a driving SRL (D-SRL) are firstly suppressed by using the double optical cross-feedback frame. Then, the chaotic output of D-SRL is injected into two response SRLs (R-SRLs) to drive the corresponding CW and CCW patterns of R-SRLs that are synchronized and bandwidth enhanced simultaneously. Thus, a bidirectional dual-channel chaos communication could be built based on chaotic synchronization of the two R-SRLs. We theoretically investigated the chaotic characteristics of a D-SRL under double optical cross-feedback and the chaotic synchronization features between R-SRL1 and R-SRL2 under different driving conditions. Results show that the time delay signatures of CW and CCW patterns of D-SRL could be effectively hidden under proper feedback conditions. The bandwidths of CW and CCW patterns of the D-SRL could be enhanced significantly. Furthermore, high-quality isochronous synchronization between R-SRL1 and R-SRL2 can be realized by choosing appropriate injection strength and detuning frequency in D-SRL and R-SRLs. Finally, the communication performances of bidirectional dual-channel chaos secure communication based on this proposed system are preliminarily examined and discussed, and the simulated results demonstrate that for 10 Gbit/s message, the Q factor of decoded message could be maintained above 6 after 10 kilometers distance transmission.