The beam-steering device is a critical component in LiDAR systems for 3D imaging. Solid-state beam-steering devices attract the most attention for their advantages of robustness, fast beam-steering speed, and stability. However, solid-state beam-steering devices, such as optical phased arrays (OPAs), are challenging to realize 2D scanning ability. Here we employed a virtually imaged phased array (VIPA) in the LiDAR system to realize all solid-state two-dimensional (2D) beam-steering based on dispersion only. A frequency swept laser source is used for performing optical frequency-modulated continuous-wave (FMCW) ranging and 2D beam steering simultaneously. The 2D disperser is compact and can be easily implemented owing to its simple structure. The mechanism of continuous scanning and ranging is beneficial for obtaining high lateral resolution, and a lateral resolution of 0.06° is achieved. 3D maps of the object at a distance of 2 m are obtained with cm-level ranging precision. The frame rate of the proposed LiDAR system only depends on the wavelength-tuning speed of the swept laser source, with the potential to realize ultrafast solid-state LiDAR systems.