Frequency-modulated continuous-wave (FMCW) lasers are the key components in FMCW LiDAR systems. In this paper, we develop and implement a rapid linearization algorithm to adaptively pre-distort the injection current, we manage to reduce the residual nonlinearity of the triangular-waveform modulated frequency down to $5.4 \times 10^{-9}$ and $4.1 \times 10^{-9}$ for down- and up-ramp frequency sweeping, respectively. The relative residual nonlinearity for down- and up-ramp frequency sweeping are 0.0020% and 0.0017%, respectively. We use this FMCW laser source with high linearity to implement a LiDAR system. We showcase three-dimensional imaging with the depth contrast and the measurement of the distance and velocity, simultaneously, of a moving object.