Promoting the sustained residence of floating population is a necessary part of accelerating the new people-centered urbanization. Housing is a place for floating population to settle down in the cities where they enter and blend into. The construction of public housing is one of the key measures to improve the living conditions of floating population, promote the process of citizenization of floating population and promote urban development. How to solve the housing problem of the floating population is not only related to meeting the requirements of the survival and development of the floating population, but also closely related to promoting the sustained residence of the floating population. Then, how about the housing situation of the floating population and its ownership of public housing? Does the ownership of public housing have any influence on the sustained residence of floating population? What is the mechanism of influence? Are there differences among groups with different flow types? Seeking answers to these questions is of great significance for promoting the sustained residence of floating population in cities, improving the level of citizenization of floating population and promoting urban development. Based on the theory of social welfare value, relative deprivation theory and planned behavior theory, this paper uses the data of China Migrants Dynamic Survey (CMDS) in 2017. Firstly, the housing status, sustained residence status, individual characteristics, employment and security characteristics as well as floating/regional characteristics of the floating population are described and analyzed, and the differences in the characteristics of sustained residence of the floating population under the status of public housing are compared. Secondly, binary Probit model and multiple linear regression model (OLS) are used to empirically test the impact of public housing on the sustained residence of floating population, and the propensity score matching method (PSM) is used to overcome the problem of selective bias in the samples. On this basis, the multiple mediating effect model is further used to explore the internal influencing mechanism. Thirdly, it compares, analyzes and explains the different types of floating population (old generation floating population, new generation floating population, rural-urban floating population, urban-urban floating population). Finally, some policy suggestions are put forward based on the research results. The main conclusions are as follows: (1) the public housing ownership rate of floating population is very low, accounting for 2.14% of the total, and there is still a long way to go in the construction of public housing for floating population. (2) Having public housing can significantly promote the sustained residence of floating population. Having public housing can significantly increase the short-term residence intention of floating population by 3.35%-3.85%, the long-term residence intention by 11.6%-14.58% and the residence time by 0.58-0.64 years. (3) Housing affordability, urban life satisfaction and sense of belonging play a mediating role in the impact of public housing on the sustained residence of floating population. (4) Heterogeneity analysis results show that public housing has a more obvious promoting effect on the sustained residence of the older generation of floating population and rural-urban floating population. Based on the above conclusions, this paper puts forward that: it is necessary for the government to continue to support the expansion of public housing coverage and supply level of floating population; We should actively innovate and broaden our thinking, flexibly use various means and methods to improve the housing affordability, urban life satisfaction and sense of belonging of floating population; Meanwhile, the limited public housing resources should be appropriately tilted to the older generation of floating population and rural-urban floating population, and the employment, income and social security status of floating population should be comprehensively improved, so as to promote the sustained residence of floating population.