Topology optimization design of steady-state heat conduction structure with interval parameters under dissipation of heat transport potential capacity constraint is discussed. The topology optimization model of heat conduction structure with interval parameter is constructed, which is based on non-probabilistic reliability with dissipation of heat transport potential capacity constraint. The total volume of heat conductive material is to be minimized and the relative thermal conductivity of elements is regarded as the design variables here. The computational expressions of numerical characteristics of dissipation of heat transport potential capacity based on interval factor method are presented. Evolutionary structural optimization method is used in the optimization. A filtering technique is employed to eliminate numerical instabilities in process of topology optimization. The numerical examples are presented to demonstrate the feasibility and effectiveness of the optimal model and solving approach.