As artificial intelligence enters the era of large models, computing power has risen from a technical tool to a strategic core resource that determines a country’s technological sovereignty, economic competitiveness, and overall security. This article aims to systematically construct a theoretical analysis framework for AI computing power sovereignty, explaining its system composition, strategic requirements, and construction path. Research shows that computing power sovereignty, as a key extension of national sovereignty in the digital space, is manifested in three dimensions: ownership, capability, and tension. In terms of ownership, computing power sovereignty is a combination of territorial jurisdiction, operational entity governance rights, and core technology dominance; in terms of capability, computing power sovereignty is a comprehensive system covering technological innovation, data supply, facility support, and institutional governance; and the realization of computing power sovereignty faces multiple practical constraints such as global supply chain, openness of the technological ecosystem, and externality of rules. Based on this, this article demonstrates the strategic requirements for building AI computing power sovereignty from four dimensions: technology, economy, security, and governance, and points out that it directly relates to a country’s survival rights, development rights, and rule-definition rights in the intelligent era. China’s construction of AI computing power sovereignty is a multi-dimensional system project covering technology, industry, facilities, elements, and rules, and requires breakthroughs in core technologies to build strong endogenous driving force, the cultivation of an industry and application ecosystem to achieve a value loop, the construction of new infrastructure to build an efficient and resilient base, the stimulation of system vitality by data and talent elements, and the shaping of international rules to gain governance initiative.