Broad spectra are of interest for a variety of applications, including pulse compression and ultrafast optical signal processing. We report a scheme of a cascaded chirped quasi-phase-matching (QPM) grating with a complementary reciprocal lattice vector bandwidth. The large reciprocal lattice vector bandwidth provided by first- and second-order QPM can simultaneously achieve second and third harmonic generations. Combined the effective nonlinear coefficient model with the transfer function method, it reveals that spectrum width increased with increasing fundamental wave bandwidth, reciprocal lattice vector bandwidth, chirp rate, and crystal length. The two-section cascaded chirped QPM grating can offer a reciprocal lattice vector bandwidth as large as 0.3 to 1.26  μm^−  1, which corresponds to a broadband spectrum covering 450 to 820 nm upon illumination with a tunable femtosecond laser. The proposed grating could extend supercontinuum generation toward potential spectroscopic applications.