Efficient access to information across multiple data types relies heavily on cross-modal retrieval of images and text. Capturing the complex relationships between these different modalities while maintaining robustness in the presence of noisy data is essential for effective retrieval. This paper proposes a novel model called Unsupervised Robust Hypergraph Correlation Hashing (URHCH) which leverages hypergraph convolutional structures and robust similarity matrices to enhance accuracy and efficiency of cross-modal hashing retrieval. Unsupervised Robust Hypergraph Correlation Hashing (URHCH) also employs affinity-enhance feature identity reconstruction techniques to improve the correlation of different modalities and enhance the modal feature. Our approach demonstrates superior performance compared to current leading methods in retrieval accuracy, as evidenced by comprehensive testing on standard benchmark datasets. Source code will provide if asked.