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Nowadays, cross-modal retrieval plays an important role to flexibly find useful information across different modalities of data. Effectively measuring the similarity between different modalities of data is the key of cross-modal retrieval. Different modalities, such as image and text, have imbalanced and complementary relationship, and they contain unequal amount of information when describing the same semantics. For example, images often contain more details that cannot be demonstrated by textual descriptions and vice versa. Existing works based on deep neural network mostly construct one common space for different modalities, to find the latent alignments between them, which lose their exclusive modality-specific characteristics. Therefore, we propose modality-specific cross-modal similarity measurement approach by constructing the independent semantic space for each modality, which adopts an end-to-end framework to directly generate the modality-specific cross-modal similarity without explicit common representation. For each semantic space, modality-specific characteristics within one modality are fully exploited by recurrent attention network, while the data of another modality is projected into this space with attention based joint embedding, which utilizes the learned attention weights for guiding the fine-grained cross-modal correlation learning, and captures the imbalanced and complementary relationship between different modalities. Finally, the complementarity between the semantic spaces for different modalities is explored by adaptive fusion of the modality-specific cross-modal similarities to perform the cross-modal retrieval. Experiments on the widely used Wikipedia, Pascal Sentence, and MS-COCO data sets as well as our constructed large-scale XMediaNet data set verify the effectiveness of our proposed approach, outperforming nine state-of-the-art methods.