The key to realizing a high-performance frequency-modulated continuous wave (FMCW) laser frequency-sweeping light source is how to extend the frequency-swept bandwidth and eliminate the effect of nonlinearity. To solve these issues, this paper designs a broadband high-linear FMCW frequency-sweeping light source system based on the combination of fixed temperature control and digital optoelectronic phase-locked loop (PLL), which controls the temperatures of the two lasers separately and attempts to achieve the coarse spectral stitching based on a time-division multiplexing scheme. Furthermore, we uses the PLL to correct the frequency error more specifically after the coarse stitching, which achieves the spectrum fine stitching and, meanwhile, realizes the nonlinearity correction. The experimental results show that our scheme can successfully achieve bandwidth expansion and nonlinearity correction, and the sweeping bandwidth is twice as much as that of the original single laser. The full-width half-maximum (FWHM) of the FMCW output is reduced from 150 kHz to 6.1 kHz, which exhibits excellent nonlinear correction performance. The relative error of the FMCW ranging system based on this frequency-swept light source is also reduced from 1.628% to 0.673%. Therefore, our frequency-swept light source with excellent performance has a promising application in the FMCW laser ranging system.