This study presents an innovative application of the Taguchi design of experiment method to optimize the structure of an Artificial Neural Network (ANN) model for the prediction of elastic properties of short fiber reinforced composites. The main goal is to minimize the computational effort required for hyperparameter optimization while enhancing the prediction accuracy. By utilizing a robust experimental design framework, the structure of an ANN model is optimized. This approach involves identifying a combination of hyperparameters that provides optimal predictive accuracy with the fewest algorithmic runs, thereby significantly reducing the required computational effort. The results suggested that the Taguchi-based developed ANN model with three hidden layers, 20 neurons in each hidden layer, elu activation function, Adam optimizer, and a learning rate of 0.001 can predict the anisotropic elastic properties of short fiber reinforced composites with a prediction accuracy of 97.71%. Then, external validation of the proposed ANN model was done using experimental data, and differences of less than 10% were obtained, indicating an appropriate predictive performance of the proposed ANN algorithm. Our findings demonstrate that the Taguchi method not only streamlines the hyperparameter tuning process but also substantially improves the algorithm's performance. These results highlight the potential of the Taguchi method as a powerful tool for optimizing machine learning algorithms, especially in scenarios where computational resources are limited. The implications of this study are far-reaching, offering insights for future research in the optimization of different algorithms for improved accuracies and computational efficiencies.