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Entity alignment aims to discover unique equivalent entity pairs with the same meaning across different knowledge graphs (KGs). Existing models have focused on projecting KGs into a latent embedding space so that inherent semantics between entities can be captured for entity alignment. However, the adverse impacts of alignment conflicts have been largely overlooked during training, thereby limiting the entity alignment performance. To address this issue, we propose a novel Conflict-aware Pseudo Labeling via Optimal Transport model (CPL-OT) for entity alignment. The key idea is to iteratively pseudo-label alignment pairs empowered with conflict-aware optimal transport (OT) modeling to boost the precision of entity alignment. CPL-OT is composed of two key components -- entity embedding learning with global-local aggregation and iterative conflict-aware pseudo labeling -- that mutually reinforce each other. To mitigate alignment conflicts during pseudo labeling, we propose to use optimal transport as an effective means to warrant one-to-one entity alignment between two KGs with the minimal overall transport cost. Extensive experiments on benchmark datasets validate the superiority of CPL-OT over state-of-the-art baselines under both settings with and without prior alignment seeds.