Non-mechanical LiDAR systems have attracted extensive research interests due to their advantages of robustness and high beam-steering speed. Recently, spectral scanning has emerged as a promising solid-state beam-steering method, which combines dispersive elements with frequency-swept laser sources to perform ultrafast beam-steering. However, swept light sources used in LiDAR systems, such as semiconductor lasers and supercontinuum sources, are usually suffering from low sweep rate, bulky and high-cost that severely hinder the development of spectral-scanning LiDAR. Here, we propose a non-mechanical spectral-scanning frequency-modulated continuous-wave (FMCW) LiDAR system based on a simple compact tunable vertical-cavity surface-emitting laser (VCSEL). The fast-swept VCSEL together with wavelength division multiplexing (WDM) technology is employed for high-speed beam-steering. Millimeter-level ranging accuracy and a lateral resolution of 0.286° with an overall depth voxel acquisition rate of 128 kHz are achieved experimentally.