Recently, the bag-of-words representation is widely applied in the image retrieval applications. In this model, visual word is a core component. However, compared with text retrieval, one major problem associated with image retrieval consists in the visual word ambiguity, i.e., a trade-off between precision and recall of visual matching. To address this problem, this paper proposes a tensor index structure to improve precision and recall simultaneously. Essentially, the tensor index is a multi-dimensional index structure. It combines the strengths of two state-of-the-art indexing strategies, i.e., the inverted multi-index as well as the joint inverted index which are initially designed for approximate nearest neighbor search problems. This paper, instead, exploits their usage in the scenario of image retrieval and provides insights into how to combine them effectively. We show that on the one hand, the multi-index enhances the discriminative power of visual words, thus improving precision; on the other hand, the introduction of multiple codebooks corrects quantization artifacts, thus improving recall. Extensive experiments on two benchmark datasets demonstrate that tensor index significantly improves the baseline approach. Moreover, when incorporating methods such as Hamming embedding, we achieve competitive performances compared to the state-of-the-art ones.