：Regional poverty is the focus of attention and research of the society, while the traditional study of poverty areas lacks attention to the southeast coast of China. Taking 64 counties in Fujian Province—a relatively developed coastal province in China's southeast coastal areas—as an example, this study constructed a measurement model of 30 indicators in three dimensions and nine vectors, and analyzed the characteristics of change and driving factors of county poverty degree in 2000 and 2016 by using the multidimensional poverty degree index (PI) and Kohonen neural network algorithm. The results show that: 1) The county development level of Fujian Province is typical among the southeast coastal provinces (Guangdong, Fujian, and Zhejiang). 2) According to the poverty degree index, the province can be divided into poor counties, disadvantaged counties, and normal counties. In general, poor counties and disadvantaged counties are found in the north and southwest, and concentrated near the peripheral areas of the province. 3) The change rates of the economic dimension, social dimension, and natural dimension of poverty indicate that most of the counties belong to the slowly deteriorating area, followed by counties with rapidly improving conditions, while the counties with slow improvement are few and scattered spatially. The change rate based on PI shows that the areas with slowly deteriorating conditions are distributed in the northern, central, and southwestern parts of Fujian Province, the areas with slowly improving conditions are distributed in western Fujian Province, while rapidly improving areas are distributed in the east coast of Fujian Province. The poverty of most poor counties are caused by economic, natural, and other factors, which have important influence on the process of poverty alleviation. 4) In 2000 and 2016, medical and health care, education level, living environment, and economic development deeply affected the contribution rate of PI. Strengthening the development and provision of public services such as infrastructure, medical and health care, and education should be the focus of current poverty alleviation efforts in Fujian Province. At the same time, the ecological environment and resource endowment also play a part in poverty alleviation. 5) There are four types of poverty factors based on contribution rate of poverty degree in different vectors: Type I is dominated by education and infrastructure, type II is dominated by economic development and living environment, type III is dominated by demographic characteristics and infrastructure, and type IV is dominated by health care and economic development. This study can be of some reference for the identification of poverty counties, and may contribute to the implementation of targeted poverty alleviation strategy.