This paper presents a novel method for training nonlinear regression models using two-sample-averaged data, where each sample is the average of input-output pairs from two i.i.d. samples. Our method leverages maximum likelihood estimation under the additive Gaussian noise and normally distributed inputs assumptions. For theoretical analysis on the likelihood, we utilize Taylor approximation and eigenvalue decomposition. We then apply Fourier transformation for better numerical calculation of the approximated likelihood. Experiments on synthetic datasets demonstrate that our method outperforms the baselines, reducing the test MSE by up to 97.07 %, which is even comparable with that of models trained with original data. Furthermore, on real-world datasets using neural networks, we confirm that our method achieves an average rank of 1.6, confirming its overall superiority. This paper establishes the foundation of averaged-data learning, which is promising for privacy-preserving machine learning.