Nonmechanical beam-steering devices are of importance to achieve fast, compact, and reliable LiDAR. We propose a 2D nonmechanical beam-steering device based on a virtually imaged phased array (VIPA) for frequency-modulated continuous-wave (FMCW) LiDAR. In the design, 2D nonmechanical beam steering and high-resolution FMCW ranging can be achieved at the same time by wavelength tuning. The design formulas of the VIPA-based 2D disperser are greatly simplified by introducing appropriate approximation, and a feasible design procedure is proposed for the first time, to the best of our knowledge. Based on the proposed method, several design examples with different optimal properties are exhibited.