Time delay signature (TDS) of an external cavity and bandwidth are two important parameters that affect the applications of chaotic lasers. In this work, the output laser from a semiconductor laser with phase-modulated optical feedback was injected into another semiconductor laser with optoelectronic feedback. The two lasers thus formed an optically injected semiconductor laser subject to optoelectronic feedback, i.e., a master-slave laser system, which can be used to reduce the TDS of a chaotic laser and increase its bandwidth. The effects of external light injection coefficient, feedback intensity, and pumping factor on the TDS of the chaotic laser output from the system were numerically studied, and the influence of the TDS of the chaotic laser output from the master laser on the TDS of the chaotic laser output from the slave laser was investigated. Moreover, the bandwidth of the chaotic laser output was investigated based on the effective suppression of TDS. Results show that this scheme can effectively reduce the TDS of the chaotic laser, and increasing the external light injection coefficient, feedback intensity, and pumping factor can widen the bandwidth of the chaotic laser.