The work aims to explore the design strategy of public facilities of intangible cultural heritage rooted in local cultural identity according to the status quo and dilemma of intangible cultural heritage inheritance. Firstly, the concept of cultural heritage was redefined from the perspective of cultural memory theory. On the one hand, its dialectical characteristics and inheritance dilemma were revealed. On the other hand, the importance of local identity construction in cultural heritage inheritance was emphasized. Then, the characteristics of the current strategy of inheriting intangible cultural heritage were summarized and supplemented from the perspective of public facility design. The effectiveness of the inheritance of intangible cultural heritage came from the inheritance strategy with "function + event + meaning interaction" as the core framework, and the design strategy of public facilities could provide materialization, normalization and daily guarantee for the inheritance of intangible cultural heritage. The cultural memory theory increases the dimensions of spatial production of cultural meaning and local cultural identity construction for intangible heritage cultural inheritance. Therefore, it should be emphasized that the design of public facilities plays a key role in the construction of intangible cultural heritage community.