A polarization-independent nonmechanical laser beam steering scheme is proposed to realize continuous two-dimensional (2D) scanning with high efficiency, where the core components are two polarization-dependent devices, which are called liquid crystal optical phased arrays (LC-OPAs). These two one-dimensional (1D) devices are orthogonally cascaded to work on the state of azimuthal and elevation steering, respectively. Properties of polarization independence as well as 2D beam steering are mathematically and experimentally verified with a good agreement. Based on the experimental setup, linearly polarized beams with different polarization angles are steered with high accuracy. The measured angular deviations are less than 5 μrad, which is on the same order of the accuracy of the measurement system. This polarization-independent 2D laser beam steering scheme has potential application for nonmechanical laser communication, lidar, and other LC-based systems.