Poverty alleviation is still remaining as the greatest challenge in the modern economic development. The heaviest part of building well-off society lies in the rural construction, especially in the poverty area. The difficulty of tackling poverty is to get rid of poverty and stabilize poverty alleviation. The research on the stability of poverty alleviation can provide important theoretical basis for enhancing the sustainability of poverty alleviation results and the pertinence of poverty alleviation policies. Based on the perspective of sustainable livelihood, the paper defined concept of "poverty alleviation stability", took Anhua County in mountainous areas of Hunan Province as an example, constructed the evaluation index system of poverty alleviation stability from four dimensions of nature, economy, ability and living conditions, classified the stability grade of farmer household by using fuzzy calculation method, and further revealed the spatial distribution characteristics and influencing factors of poverty eradication stability. At last, a scientific path to improve poverty alleviation stability was explored from the perspective of economic transformation in poor areas. The results show that: 1 ) Slope and income level are the main factors that affect the stability of poverty alleviation in Anhua County, while the lack of development ability is the fundamental reason for the instability of poverty alleviation. Anhua County is a typical poverty-stricken county in mountainous area, and an in-depth analysis of Anhua County poverty alleviation stability was conducted for finding the leading factors of poverty alleviation, so as to provide reference for enhanceing the ability of farmers to get rid of poverty and achieveing stable poverty alleviation of poor farmers in mountainous areas. The index weights of slope and income stability are 24.88% and 14.61% respectively, which are the main factors affecting the stability of poverty alleviation in Anhua County. The index weights of education guarantee and nutrition status are 13.60% and 10.91% respectively, which are the secondary important factors affecting the stability of poverty alleviation. 2) The stability of poverty eradication in Anhua County is overall good. The farmer households with less stable poverty alleviation are mainly distributed in the high mountain and steep slope areas, and the poverty alleviation stability is closely related to the geographical environment. In terms of spatial position, the concentrated distribution areas of relatively less stable poverty alleviation are coincide with several important ecological function areas. Poverty alleviation should be combined with the construction of ecological function areas. In terms of vertical zonation of spatial distribution, the farmer household of less stable poverty alleviation concentrated in the high mountains and steep slope areas. However, the stability of poverty alleviation index of farmer households in intermountain valleys is generally high, which indicates that the stability of poverty alleviation is closely related to the geographical environment. 3) This study is mainly aimed at poverty alleviation in poor counties in mountainous areas. The main proposals to enhance the stability of poverty alleviation includes: relying on the advantages of natural resources to develop characteristic industries, stimulating the regional endogenous development momentum; further improving regional infrastructure conditions, the level of rural public service facilities, the livelihoods of rural households out of poverty, the level of knowledge and skills of rural residents. And the improving of the rural population quality is the key to cultivate long-term ability to become rich, optimize the layout of rural settlements in combination with the relocation of poverty alleviation and the renovation of "hollow villages".