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Multi-modal entity alignment aims to identify equivalent entities between two different multi-modal knowledge graphs, which consist of structural triples and images associated with entities. Most previous works focus on how to utilize and encode information from different modalities, while it is not trivial to leverage multi-modal knowledge in entity alignment because of the modality heterogeneity. In this paper, we propose MCLEA, a Multi-modal Contrastive Learning based Entity Alignment model, to obtain effective joint representations for multi-modal entity alignment. Different from previous works, MCLEA considers task-oriented modality and models the inter-modal relationships for each entity representation. In particular, MCLEA firstly learns multiple individual representations from multiple modalities, and then performs contrastive learning to jointly model intra-modal and inter-modal interactions. Extensive experimental results show that MCLEA outperforms state-of-the-art baselines on public datasets under both supervised and unsupervised settings.