Online Continual Learning (OCL) empowers machine learning models to acquire new knowledge online across a sequence of tasks. However, OCL faces a significant challenge: catastrophic forgetting, wherein the model learned in previous tasks is substantially overwritten upon encountering new tasks, leading to a biased forgetting of prior knowledge. Moreover, the continual doman drift in sequential learning tasks may entail the gradual displacement of the decision boundaries in the learned feature space, rendering the learned knowledge susceptible to forgetting. To address the above problem, in this paper, we propose a novel rehearsal strategy, termed Drift-Reducing Rehearsal (DRR), to anchor the domain of old tasks and reduce the negative transfer effects. First, we propose to select memory for more representative samples guided by constructed centroids in a data stream. Then, to keep the model from domain chaos in drifting, a two-level angular cross-task Contrastive Margin Loss (CML) is proposed, to encourage the intra-class and intra-task compactness, and increase the inter-class and inter-task discrepancy. Finally, to further suppress the continual domain drift, we present an optional Centorid Distillation Loss (CDL) on the rehearsal memory to anchor the knowledge in feature space for each previous old task. Extensive experimental results on four benchmark datasets validate that the proposed DRR can effectively mitigate the continual domain drift and achieve the state-of-the-art (SOTA) performance in OCL.