A linear frequency modulation laser is the core device of frequency modulated continuous wave (FMCW) lidar, and the frequency modulation linearity of the laser affects the ranging accuracy and resolution performance of FMCW lidar. This study first suppressed the frequency modulation nonlinearity of lasers and subsequently designed a distributed feedback (DFB) laser frequency modulation nonlinearity correction system based on a field programmable gate array (FPGA). Here, a pre-distortion iterative control learning algorithm acts as the core of the system. In real time, the system can detect the nonlinearity of the laser and optimize its injection current based on nonlinear distortion, thereby significantly reducing the frequency modulation nonlinearity of the DFB laser. A linear frequency modulation DFB laser with a scanning frequency of 5 kHz and a modulation bandwidth of 1.2 GHz is achieved using this method. The nonlinearity of the up and down sweep cycles of the DFB laser is reduced from 2.62% and 1.96% to 0.035% and 0.031%, respectively. Ranging experiments were conducted using the developed linear frequency modulation DFB laser, where the maximum error within 5 m is less than 14 mm.