Federated learning (FL) in healthcare allows the collaborative training of models on distributed data sources, while ensuring privacy and leveraging collective knowledge. However, as each institution collects data separately, conventional FL cannot leverage the different features depending on the institution. We proposed a personalized progressive FL (PPFL) approach that leverages client-specific features and evaluated with real-world datasets. We compared the performance of in-hospital mortality prediction between our model and conventional models based on accuracy and area under the receiver operating characteristic (AUROC). PPFL achieved an accuracy of 0.941 and AUROC of 0.948, which were higher than the scores of the local models and FedAvg algorithm. We also observed that PPFL achieved a similar performance for cancer data. We identified client-specific features that can contribute to mortality. PPFL is a personalized federated algorithm for heterogeneously distributed clients that expands the feature space for client-specific vertical feature information.