Using a semiconductor laser subjected to optical feedback from cascaded chirped fiber Bragg gratings (CFBGs), we propose and demonstrate a method for generating wideband chaos without a time-delay signature (TDS). The high dispersion of cascaded CFBGs creates irregular external-cavity modes and destroys the resonance of external-cavity mode, eliminating the TDS of the chaotic signal. In addition, the irregular external-cavity modes beat with the internal-cavity modes of the laser, introducing new high-frequency oscillations, which enhances the bandwidth of the chaotic signal. The effects of the dispersive optical feedback strength and wavelength detuning between the laser and CFBG on bandwidth and TDS in feedback systems with single CFBG and cascaded CFBGs were compared in the experiment. The obtained results show that the feedback system with cascaded CFBGs exhibits better performances in bandwidth improvement and TDS suppression under strong feedback and negative wavelength detuning conditions. Finally, we experimentally obtained a TDS-free chaotic signal with a 3 dB bandwidth of 12 GHz.