The main form of China's poverty problem has shifted from absolute poverty to relative poverty. Conforming to the needs of relative poverty governance, it is necessary to systematically construct the logic and mechanism of governance. Based on the analysis of the concept, characteristics and governance needs of relative poverty, the article starts from the systematic concept, refines and explains the “1+4” logic of relative poverty management, which takes the party leadership as the core and takes autonomy, rule of law, co-governance and technological governance as the means. The cases of “ecological poverty alleviation” in Anji, Zhejiang Province and “Luliang Mountain nurse workers” in Shanxi Province show that the basic conditions for promoting common prosperity are different, and the focus of governance will be different. Anji attaches great importance to the construction of green development concept and the demonstration mechanism of common prosperity. Luliang attaches great importance to the employment training of nursing workers and the construction of poverty alleviation and income increase mechanism. However, there is a consensus on its governance logic, as both take the institutional advantages of socialism with Chinese characteristics and the leadership of the Party to promote local governance efficiency. Therefore, on the basis of the “1+4” logic, the article summarizes the basic framework of the long-term mechanism of poverty governance from six aspects: organizational mechanism, internal motivation mechanism, legal mechanism, collaborative co-governance mechanism, monitoring mechanism, and demonstration and leading mechanism. It is intended to provide a governance example for the nation to promote common prosperity.