This paper presents an effective framework for predicting magnetic properties and optimizing the material design of Mn-Zn ferrite core. The objective of the current work is to construct a high-accuracy machine learning-based surrogate model correlating the configuration parameters of ferrite core and its electromagnetic performance according to the various material composition. The finite element method (FEM) combined with a model that considers the dielectric effect was developed to analyze dimensional resonance by magnetic simulation. The dielectric effect was treated as the equivalent circuit and was formulated by coupling with Maxwell's equations. To accelerate evaluating performance, we construct an ANNbased FE surrogate model. Training data is generated through the FEM-based electromagnetic analysis framework, and analysis-based data is added to the previous experimental-based data. ANN models were trained to predict microstructure parameters, magnetic properties, and core loss using expanded data. Finally, the Mn-Zn ferrite core performance for various compositions can be mapped through the effective surrogate model and identifies material compositions with optimized magnetic properties. Therefore, the magnetic properties are effectively calculated by the trained neural network, and the optimized composition of the ferrite core shows that the proposed framework can significantly improve the efficiency of material design.