Aiming at the problems of limited bandwidth and obvious time-delay signature (TDS) of monolithically integrated chaotic semiconductor lasers, this paper proposes a four-segment InP-based monolithically integrated chaotic semiconductor laser. The laser structure is composed of a distributed feedback (DFB1) laser region, a semiconductor optical amplifier (SOA) region, a distributed Bragg reflector (DBR) grating region and a distributed feedback (DFB2) laser region. Mutual injection between the two DFB laser regions effectively enhances the bandwidth of power spectrum. The DBR grating region is used to form a complex multi-feedback cavity to suppress the TDS caused by the fixed external cavity structure. The simulation results show that the chaotic signal with the standard bandwidth of 29.2 GHz and the TDS value of 0.094 is generated. The research in this paper can further improve the performance of monolithically integrated chaotic laser, and provide a high-quality chaotic laser source for secure optical communication, chaotic lidar and distributed optical fiber sensing.