2020 is the decisive year of poverty alleviation. China has made remarkable achievements in poverty alleviation, but how to prevent the phenomenon that poor households return to poverty after poverty alleviation is a very urgent research topic at this stage. Under the theory of evolutionary game, this paper establishes a game model between the governments and the families out of poverty, and solves the evolutionary stability strategy. The results show that: without constraints, the outcome of the evolutionary game will evolve in two different directions. One is the rational state we desire, that is, governments are incentive and poor households are positive, the other is an unreasonable state, that is, the governments are non-incentive and poor households are negative. Finally, suitable suggestions are put forward to make the game evolve to a reasonable result by analyzing the relevant parameters.