A new closed-loop dual-directionally chaotic system with three lasers for private message transmission is proposed. A pair of twin semiconductor lasers as responses are routed into chaos by delayed optical feedback, and chaos synchronization to each other is realized by means of optical injection of a common chaotic-driving signal generated by a drive laser subject to delayed optical feedback. Appropriate model is built. We investigate the bifurcation and synchronization performance and the effect of internal parameter mismatch, and the results are compared with those of the open-loop system in which the response lasers are not subject to local feedback. The theoretical simulations show thatthe maximum value of cross correlation coefficient between two responses approximates to 1, however, the maximum value of cross correlation coefficient for response and driver is very low. Compared with the open-loop system, the bandwidth of the designed system is widened by about 1.99 GHz, and this system becomes more sensitive to parameter mismatch. So the closed-loop scheme offers a better privacy level.