To address the modality learning degeneration caused by modality imbalance, existing multimodal learning~(MML) approaches primarily attempt to balance the optimization process of each modality from the perspective of model learning. However, almost all existing methods ignore the modality imbalance caused by unimodal data sampling, i.e., equal unimodal data sampling often results in discrepancies in informational content, leading to modality imbalance. Therefore, in this paper, we propose a novel MML approach called \underline{D}ata-aware \underline{U}nimodal \underline{S}ampling~(\method), which aims to dynamically alleviate the modality imbalance caused by sampling. Specifically, we first propose a novel cumulative modality discrepancy to monitor the multimodal learning process. Based on the learning status, we propose a heuristic and a reinforcement learning~(RL)-based data-aware unimodal sampling approaches to adaptively determine the quantity of sampled data at each iteration, thus alleviating the modality imbalance from the perspective of sampling. Meanwhile, our method can be seamlessly incorporated into almost all existing multimodal learning approaches as a plugin. Experiments demonstrate that \method~can achieve the best performance by comparing with diverse state-of-the-art~(SOTA) baselines.