Using a semiconductor laser with double optical feedback as a chaos transmitter, a unidirectional chaotic synchronization communication system is constructed, and the performances of such a system are investigated numerically. The results show that by selecting reasonable parameters, the time delay behaviour of chaotic carrier generated by the semiconductor laser with double optical feedback can be suppressed efficiently; through the strong injection from transmitter to receiver, the perfect synchronization between transmitter and receiver can be realized, and the synchronization quality has a high tolerance to frequency detuning between transmitted laser and received laser; under the additive chaos modulation encryption scheme, the 500 Mbits/s encoded message can be hidden efficiently in the chaotic carrier and successfully extracted at the receiver.