Semiconductor laser (SL) can output chaotic lasers under external disturbances such as optical injection or optical feedback, and the bandwidth can reach up to GHz magnitude. External-cavity feedback semiconductor lasers can output high-dimensional chaotic lasers and are considered to be better sources of chaotic entropy. However, due to external cavity feedback and other effects, it will give rise to obvious external cavity time delay signature (TDS) in the output chaotic laser, which restricts the application of chaotic lasers. On the other hand, the bandwidth of chaotic laser determines the transmission rate of confidential communication, and therefore TDS and bandwidth are two important parameters that will affect chaotic laser’s applications. Therefore, it is significant to take appropriate measures to suppress the TDS and increase the bandwidth of chaotic laser output by semiconductor laser.In this paper the output laser from a semiconductor laser with single optical feedback is partially injected to another semiconductor laser with double filtered optical feedback. Thus they form a semiconductor laser system with external optical injection and double filtered optical feedback, i.e. a master-slave laser system which is used to suppress the TDS of chaotic laser and investigate its bandwidth. We numerically investigate the influences of external light injection coefficient, feedback intensity, pumping factor, and filter bandwidth on TDS. Then the suppression effects of this system on TDS are analyzed and compared with those of semiconductor laser system with external optical injection and single optical feedback, those of semiconductor laser system with external optical injection and double optical feedback, those of semiconductor laser system with external optical injection and single filtered optical feedback, and those of semiconductor laser system with double filtered optical feedback. The results show that the proposed scheme in this paper has the best suppression effect on TDS. Then the bandwidth of the chaotic laser output from the system is investigated under the condition of parameters of effectively suppressing TDS. The results show that the system proposed in this paper can increase the bandwidth of the system output chaotic laser by properly selecting the parametric values, and the maximum bandwidth value of the obtained chaotic laser is about 8.8 GHz. The above investigations indicate the effectiveness of the proposed scheme. The results of this investigation are significant for the application of chaotic lasers.