Clinical predictive models often rely on patients electronic health records (EHR), but integrating medical knowledge to enhance predictions and decision-making is challenging. This is because personalized predictions require personalized knowledge graphs (KGs), which are difficult to generate from patient EHR data. To address this, we propose GraphCare, an open-world framework that leverages external KGs to improve EHR-based predictions. Our method extracts knowledge from large language models (LLMs) and external biomedical KGs to generate patient-specific KGs, which are then used to train our proposed Bi-attention AugmenTed BAT graph neural network GNN for healthcare predictions. We evaluate GraphCare on two public datasets: MIMIC-III and MIMIC-IV. Our method outperforms baseline models in four vital healthcare prediction tasks: mortality, readmission, length-of-stay, and drug recommendation, improving AUROC on MIMIC-III by average margins of 10.4%, 3.8%, 2.0%, and 1.5%, respectively. Notably, GraphCare demonstrates a substantial edge in scenarios with limited data availability. Our findings highlight the potential of using external KGs in healthcare prediction tasks and demonstrate the promise of GraphCare in generating personalized KGs for promoting personalized medicine.