Vertical federated learning has gained popularity as a means of enabling collaboration and information sharing between different entities while maintaining data privacy and security. This approach has potential applications in disease healthcare, cancer prognosis prediction, and other industries where data privacy is a major concern. Although using multi-omics data for cancer prognosis prediction provides more information for treatment selection, collecting different types of omics data can be challenging due to their production in various medical institutions. Data owners must comply with strict data protection regulations such as European Union (EU) General Data Protection Regulation. To share patient data across multiple institutions, privacy and security issues must be addressed. Therefore, we propose an adaptive optimized vertical federated-learning-based framework adaptive optimized vertical federated learning for heterogeneous multi-omics data integration (AFEI) to integrate multi-omics data collected from multiple institutions for cancer prognosis prediction. AFEI enables participating parties to build an accurate joint evaluation model for learning more information related to cancer patients from different perspectives, based on the distributed and encrypted multi-omics features shared by multiple institutions. The experimental results demonstrate that AFEI achieves higher prediction accuracy (6.5% on average) than using single omics data by utilizing the encrypted multi-omics data from different institutions, and it performs almost as well as prognosis prediction by directly integrating multi-omics data. Overall, AFEI can be seen as an efficient solution for breaking down barriers to multi-institutional collaboration and promoting the development of cancer prognosis prediction.