During the restoration process of primary restorative transmission system, some over voltages may happen due to nonlinear interaction between unloaded transformers and transmission systems. These over voltages caused by harmonic resonance can be suppressed by inserting damping loads before energizing transformers. But it is very difficult to predict the occurrence possibility of harmonic resonance and complex simulation must be repeated to estimate the sufficient damping loads. This paper presents a damping loads prediction system to prevent harmonic resonance. Detailed analysis of the relationship between harmonic resonance and the amount of damping loads is discussed. The prediction system is developed using a curve fitting and a neural network based on this relationship. A curve fitting used a Gaussian function based on non-linear least square method and multi-layer back-propagation neural network is applied. The system is applied to primary restorative transmission lines in korean power system and the result showed satisfactory performance.