Food security is a serious global issue, concerning the availability, accessibility, safety, and stability of food. The agri-food supply chain, which connects farms to consumers, often faces problems such as fragmented data systems, poor transparency, and low trust between stakeholders. These problems make decision-making slow and reduce the quality and safety of food. During the Fourth Industrial Revolution (IR4.0), digital technologies are transforming many industries, including food sector. Among them, blockchain has emerged as a critical enabler for traceability and accountability. However, balancing transparency and privacy remains a major challenge as sensitive business data must be protected. Without solving this issue, many stakeholders are not ready to accept blockchain solutions. This study analyses current blockchain limitations and proposes a privacy-preserving blockchain solution for agri-food supply chains. Using the Design Science Research Methodology (DSRM), this work identifies key privacy gaps, designs a solution integrating selective data sharing, access control, and privacy-preserving techniques such as zero-knowledge proofs and differential privacy and outlines future empirical validation through prototype implementation. These features aim to balance open traceability with the need to keep important information private. The results suggest that a privacy-preserving blockchain can enhance trust, protect private data, and maintain transparency in the food chain. This makes the system more resilient and reliable. At the same time, it supports the United Nations goals, especially Goal 2 (Zero Hunger) and Goal 12 (Responsible Consumption and Production), by helping to build food supply chains that are safe, fair, and sustainable.