Light detection and ranging (LiDAR) is the enabling sensor for high-resolution three- dimensional (3D) imaging. It has been widely used in scientific research, industrial metrology, robotics, autonomous vehicles, and consumer electronics. Compared with the conventional pulsed time-of-flight LiDAR, the frequency-modulated continuous-wave (FMCW) LiDAR requires lower optical power, lower electronic bandwidth, and is intrinsically immune to the interference from the ambient light and other LiDAR units due to the coherent detection mechanism. However, an FMCW LiDAR typically requires a linearly frequency-chirped laser with low phase noise, which are conventionally realized by complicated feedback control circuits. In this work, we report on linearizing the laser chirp by the iterative learning pre-distortion method and compensating for the phase noise by processing the signal with the help of a monitor interferometer. Experimental results with a commercial distributed feedback (DFB) laser show that with the pre-distortion linearization method, the relative residual nonlinearity of the laser chirp can be reduced to less than 0.003%, and the post-processing phase noise compensation can extend the LiDAR detection range to more than 250 m. With the proposed methods, high-performance and low-cost FMCW LiDAR systems can be achieved without requiring expensive narrow-linewidth lasers or complex controllers.