We proposed and numerically verified a method of generating broadband chaotic signals using a dual-mode distributed feedback (DM-DFB) semiconductor laser with optical feedback. A theoretical model of the laser was established according to the dual-longitudinal-mode Lang-Kobayashi equation. It was determined that the generation mechanism of the broadband chaotic signals was the mode beat effect. The influences of mode interval, bias current, and feedback coefficient on the chaotic signal bandwidth were numerically investigated. Subsequently, a dual-mode laser was designed by simulation. In the mirror feedback system, a chaotic signal with a bandwidth of 38.6 GHz was generated under a high bias current and strong feedback intensity. The structure provides a new idea for broadband integrated chaotic sources.