Label noise is ubiquitous in real-world scenarios, posing a practical challenge to supervised models due to its effect in hurting the generalization performance of deep neural networks. Existing methods primarily employ the sample selection paradigm and usually rely on dataset-dependent prior knowledge (e.g., a pre-defined threshold) to cope with label noise, inevitably degrading the adaptivity. Moreover, existing methods tend to neglect the class balance in selecting samples, leading to biased model performance.To this end, we propose a simple yet effective approach named SED to deal with label noise in a Self-adaptivE and class-balanceD manner. Specifically, we first design a novel sample selection strategy to empower self-adaptivity and class balance when identifying clean and noisy data. A mean-teacher model is then employed to correct labels of noisy samples. Subsequently, we propose a self-adaptive and class-balanced sample re-weighting mechanism to assign different weights to detected noisy samples. Finally, we additionally employ consistency regularization on selected clean samples to improve model generalization performance. Extensive experimental results on synthetic and real-world datasets demonstrate the effectiveness and superiority of our proposed method.