The center wavelength of the distribution feedback semiconductor laser is about 1550 nm, and it is in the lowest loss window of the optical fiber communication. A distribution feedback semiconductor laser (DFB-SL) can generate wideband chaotic signals under external disturbances such as optical feedback, optical injection, etc. Thus, due to the simple structure, DFB-SLs with the optical feedback are widely applied to many fields, including information security, lasers radar, and physical entropy sources for generating physical random numbers. However, optical feedback can cause weak periodicity in chaotic signals from the semiconductor laser, and increase the time delay characteristics of chaotic laser, moreover reduce the quality of random numbers generated by using chaotic signals. Meanwhile, to meet the needs of the current high speed and large capacity communication, the DFB-SL, which can generate wideband chaotic laser with low time delay characteristics, has received wide attention and become a hot research subject.In this paper, we present a new scheme for suppressing the time delay characteristics and investigating the bandwidth (BW) of chaotic signals from the semiconductor laser. In this scheme, we build a system that is a distribution feedback semiconductor laser with double phase modulated optical feedback (DFB-SL-DPMOF). In this system, two phase modulators driven by the pseudorandom signals are respectively added to the two optical feedback cavities to eliminate the weak periodicity of the generated chaotic signals. For this system, we numerically investigate the influence of the system parameter, such as the delay time, feedback coefficient, etc., on the time delay characteristic of the chaotic laser. In this paper, the time delay characteristic of chaotic signal is expressed by the maximum value of the time delay signature (TDS) peak of the autocorrelation function curve. Then, to illuminate the effectiveness of this system, other two systems, i.e., DFB-SL with double optical feedback (DFB-SL-DOF) and DFB-SL with single phase modulated optical feedback (DFB-SL-SPMOF) are considered. We study the suppression effect of the system on the TDS among DFB-SL-DPMOF, DFB-SL-DOF and DFB-SL-SPMOF. For these three systems, we give and analyze the simulation curves of the time delay characteristic values with the feedback coefficient and the pumping factor respectively. The results indicate that our proposed scheme has the best suppression effect. Moreover, we numerically investigate the BW of chaotic signals from DFB-SL-DPMOF based on the parameter conditions suppressing TDS effectively. The results show that BW becomes large with the pumping factor and feedback coefficient increasing, and the maximum BW value of the obtained chaotic laser is about 7.2 GHz. Therefore the effectiveness of the presented scheme is numerically clarified. And the conclusions of this paper are useful for applying the chaotic laser to the secure communication field.