In the rapidly evolving domain of artificial intelligence (AI) technologies, integrating Human-Centered Artificial Intelligence (HCAI) within service science is increasingly pivotal for enhancing service sector performance. This paper introduces a methodological framework for HCAI service design, called HCAI-SD framework, a novel approach that incorporates HCAI principles into service science to facilitate the design of HCAI services. The framework prioritizes the harmonization of AI capabilities with human-centered design principles and HCAI guidance. While using a design science methodology, the framework effectively addresses the unique requirements of HCAI services by integrating insights from different levels of service science, including the value creation network, service system, and service levels. To demonstrate the application of the framework in a real-world scenario, a comprehensive case study is presented that aims at designing an HCAI service to enhance the systematic literature review process in the domain of AI in education. This research contributes significantly to the integration of AI capabilities within service science and provides a methodological framework for developing robust and complex HCAI services.