To analyze the relationship between the spatial light modulation characteristics of a liquid crystal phased array and the driving voltage using the liquid crystal continuous elastic deformation theory, in this paper, a method for solving the spatial distribution of a differential iteration liquid crystal director was proposed based on nonlinear least squares. Based on the electro-optical properties of the liquid crystal material, the distribution of the liquid crystal director at the threshold voltage was used as the initial value. For the direct calculation of the component of the potential shift vector along the Z axis with the driving voltage, the director space distribution of the liquid crystal was deduced under the action of an applied electric field. The phase modulation characteristic curve of the liquid crystal phase delay versus the applied voltage in the steady state was plotted. Finally, the theory was verified experimentally. Far-field beam pointing deflection control was achieved by controlling the driving voltage of the liquid crystal phased array. Using the driving voltage to directly solve the electric displacement vector, the initial value of the coupling between the director and potential shift was provided. This not only simplified the calculation but also accords with the motion process of the liquid crystal molecule under the action of the actual electric field as well as reduced the model error. The simulation results show that when the system error is 1.0×10-8, the mean time of iteration is 0.33 s under different voltages. When the driving voltage is 5 V, the angular error precision of the tilt angle of the liquid crystal molecules is improved by 0.09 rad compared to that achieved with the direct difference iteration method.