We propose and demonstrate a frequency modulated continuous-wave (FMCW) light detection and ranging (LiDAR) system, which employs double-sideband modulation combining with injection-locking to generate triangular linear frequency modulation light source. A fiber laser working as master laser is modulated by a Mach-Zehnder modulator to produce two first-order sidebands with tuning range of 8–14 GHz, one of which is extracted and amplified by a slave distributed feedback laser. A large carrier suppression ratio up to 20 dB is realized. The experiment results show the spatial resolution of the proposed LiDAR is 2.5 cm, equaling to the theoretical value. The velocity measurement is also performed by extracting Doppler shift. Finally, by combining the proposed LiDAR with 2-axis mechanical galvanometer scanner, the 3D imaging with high precision is realized, and the real scene is well restored. The proposed LiDAR system realizes pure linear frequency modulation without complex linearization algorithm or clock sampling circuit, and has advantages of simple structure and high precision.