Abstract: Topology optimization design of planar continuum structure with fuzzy parameters under fuzzy loads is discussed. Fuzzy variables are transformed into random variables by information entropy. Mathematical model of topology optimization of continuum structures with random parameters under random loads is established. The topology optimization model is constructed based on probability, where the stress constraints are transformed into equivalent normal constraints, while the structural weight is to be minimized and the elemental design variables for the structural topology description are considered. The computational expressions of numerical characteristics of stress responses based on random factor method are presented. Bi-directional evolutionary structural optimization method is used in the optimization. Two examples have been used to illustrate the feasibility and effectiveness of the optimal model and the proposed method.