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Despite significant progress over the past few years, ambiguity is still a key challenge in Facial Expression Recognition (FER). It can lead to noisy and inconsistent annotation, which hinders the performance of deep learning models in real-world scenarios. In this paper, we propose a new uncertainty-aware label distribution learning method to improve the robustness of deep models against uncertainty and ambiguity. We leverage neighborhood information in the valence-arousal space to adaptively construct emotion distributions for training samples. We also consider the uncertainty of provided labels when incorporating them into the label distributions. Our method can be easily integrated into a deep network to obtain more training supervision and improve recognition accuracy. Intensive experiments on several datasets under various noisy and ambiguous settings show that our method achieves competitive results and outperforms recent state-of-the-art approaches. Our code and models are available at https://github.com/minhnhatvt/label-distribution-learning-fer-tf.