Little research focuses on cross-modal correlation learning where temporal structures of different data modalities such as audio and lyrics are taken into account. Stemming from the characteristic of temporal structures of music in nature, we are motivated to learn the deep sequential correlation between audio and lyrics. In this work, we propose a deep cross-modal correlation learning architecture involving two-branch deep neural networks for audio modality and text modality (lyrics). Different modality data are converted to the same canonical space where inter modal canonical correlation analysis is utilized as an objective function to calculate the similarity of temporal structures. This is the first study on understanding the correlation between language and music audio through deep architectures for learning the paired temporal correlation of audio and lyrics. Pre-trained Doc2vec model followed by fully-connected layers (fully-connected deep neural network) is used to represent lyrics. Two significant contributions are made in the audio branch, as follows: i) pre-trained CNN followed by fully-connected layers is investigated for representing music audio. ii) We further suggest an end-to-end architecture that simultaneously trains convolutional layers and fully-connected layers to better learn temporal structures of music audio. Particularly, our end-to-end deep architecture contains two properties: simultaneously implementing feature learning and cross-modal correlation learning, and learning joint representation by considering temporal structures. Experimental results, using audio to retrieve lyrics or using lyrics to retrieve audio, verify the effectiveness of the proposed deep correlation learning architectures in cross-modal music retrieval.