Liquid crystal spatial light modulators (LC-SLMs) are usually polarization sensitive optical elements. In this paper, we propose a polarization-independent beam steering system to overcome the polarization problem of conventional liquid crystal devices by employing two polarization-dependent LC-SLMs, a polarizing beam splitter and a half-wave plate. In this system, two one-dimensional LC-SLMs are aligned orthogonally to deflect the beam in azimuthal and elevation, respectively. This system enables LC-SLMs to work in any polarization state of incident light, and can realize continuous two-dimensional laser beam pointing. Properties of polarization-independence as well as two-dimensional beam steering were mathematically and experimentally verified with a good agreement. Using the well aligned beam steering system, linearly polarized beams in different polarization angle are deflected with high accuracy and efficiency. The measured angular deviations are less than 5 micro-radians to show a high-accuracy beam steering of the system. This polarization-independent beam steering scheme is useful in the applications of nonmechanical laser communication, Lidar, and other LC-based devices.