Fairness is now an important issue in machine learning. There are arising concerns that automated decision-making systems reflect real-world biases. Although a wide range of fairness-related methods have been proposed in recent years, the under-representation problem has been less studied. Due to the uneven distribution of samples from different populations, machine learning models tend to be biased against minority groups when trained by minimizing the average empirical risk across all samples. In this paper, we propose a novel adaptive reweighing method to address representation bias. The goal of our method is to achieve group-level balance among different demographic groups by learning adaptive weights for each sample. Our approach emphasizes more on error-prone samples in prediction and enhances adequate representation of minority groups for fairness. We derive a closed-form solution for adaptive weight assignment and propose an efficient algorithm with theoretical convergence guarantees. We theoretically analyze the fairness of our model and empirically verify that our method strikes a balance between fairness and accuracy. In experiments, our method achieves comparable or better performance than state-of-the-art methods in both classification and regression tasks. Furthermore, our method exhibits robustness to label noise on various benchmark datasets.