Integration of heterogeneous and high-dimensional multi-omics data is becoming increasingly important in understanding genetic data. Each omics technique only provides a limited view of the underlying biological process and integrating heterogeneous omics layers simultaneously would lead to a more comprehensive and detailed understanding of diseases and phenotypes. However, one obstacle faced when performing multi-omics data integration is the existence of unpaired multi-omics data due to instrument sensitivity and cost. Studies may fail if certain aspects of the subjects are missing or incomplete. In this paper, we propose a deep learning method for multi-omics integration with incomplete data by Cross-omics Linked unified embedding with Contrastive Learning and Self Attention (CLCLSA). Utilizing complete multi-omics data as supervision, the model employs cross-omics autoencoders to learn the feature representation across different types of biological data. The multi-omics contrastive learning, which is used to maximize the mutual information between different types of omics, is employed before latent feature concatenation. In addition, the feature-level self-attention and omics-level self-attention are employed to dynamically identify the most informative features for multi-omics data integration. Extensive experiments were conducted on four public multi-omics datasets. The experimental results indicated that the proposed CLCLSA outperformed the state-of-the-art approaches for multi-omics data classification using incomplete multiomics data.