A dual-core-bidirectional optical fiber chaotic secure communication system is proposed based on coupling-feedback synchronization of chaotic injected multi-quantum well (MQW) laser systems with fiber channels for optical fiber secure communications. A physical model of the system is built using dual-core optical fiber connecting the transmitter and receiver. Chaotic synchronization was theoretically and numerically studied and we found theoretically that self-phase modulation in the fiber would limit the chaotic synchronization. The nonlinear phase shift, power limit and propagation length are formulated. Chaotic synchronization of two long-distance fibers was numerically achieved, and synchronization time varying with fiber propagation length was numerically analysed. Optical fiber chaotic communications and their synchronization errors were numerically simulated in long-distance dual-core-bidirectiond optical fiber chaotic secure communications with an analog signal of modulation frequency 06 GHz, a digital signal of modulation rate 06 bit/s and a bit rate of 005 Gbit/s of chaos keying shift, respectively. The system bandwidth is also numerically analysed. The system has a good security capability of application in dual-core-bidirectional fiber secure communications.