The voltage unbalance at the load terminal of three-phase electric power system is discussed. The aim of this work is to solve the problem of voltage unbalance accurately and quickly by using the Neural Network Control (NNC). In this paper, the Aqaba-Qatrana-South Amman (AQSA) power system is considered and modelled as a real case study. The three RMS-Load Voltages (3RMSLV) and the Voltage Unbalance Factor (VUF) for different unbalance conditions are collected. In addition, the corresponding firing angles (FATCR) required to drive the Thyristor-Controlled-Reactor (TCR) compensator for balanced condition are determined. These data are used to train, validate, and test the NNC. The NNC training depends on the fact that each unbalance condition has its own 3RMSLV and VUF and needs a unique set of FATCR for getting back the balance condition. Several test cases were discussed to validate the capability of the proposed method in solving the voltage unbalance problem.