Liquid crystal microwave phased arrays (LC-MPAs) are regarded as an ideal approach to realize compact antennas owing to their advantages in cost, size, weight, and power consumption. However, the shortcoming in low radiation deflection efficiency has been one of LC-MPAs’ main application limitations. To optimize the steering performance of LC-MPAs, it is essential to model the channel imperfections and compensate for the phase errors. In this paper, a phase error estimation model is built by training a neural network to establish a nonlinear relationship between the near-field phase error and the far-field pattern, hence realizing fast calibration for LC-MPAs within several measured patterns. Simulations and experiments on a 64-channel, two-dimensional planar antenna were conducted to validate this method. The results show that this method offers precise phase error estimations of 3.58° on average, realizes a fast calibration process with several field-measured radiation patterns, and improves the performances of the LC-MPA by approximately 4%–10% in deflection efficiency at different steering angles.