Structure topology optimization, which is an important part of structure design, is becoming more and more important in recent years. At present, the research on structure topology optimization is mainly based on the theory of material linearity, in which the deformation of material is assumed linear. However, the nonlinear behavior of material occurs inevitably in practical engineering structures, such as house structure in earthquake area. It is demanded that the house can not be destroyed within a certain range of earthquke load. Therefore, the material nonlinearity must be taken into account in the research of structure topology optimization, so that the more practical topology structure can be obtained. In this paper, a review of researches on structure topology optimization with material nonlinearity was stated, and a brief expectation was presented.