In New Zealand, health equity is a pressing concern, and reaching disadvantaged populations has become the goal to close the inequity gap. Building and strengthening health systems is one way to secure better outcomes. However, the discourse to date has predominately focussed on inequities in health outcomes for Māori. This study has an interest in the African ethnic minority community in New Zealand. It undertakes a narrative review of the New Zealand health system which aims to identify literature around the attainment of health equity of African minority by (i) providing a critical overview of the healthcare delivery system using the World Health Organization’s six inter-related building blocks of health system strengthening; (ii) developing a summary and discussions of the research results and; (iii) identifying priorities and recommendations for future research.