The topology optimization of variable density method was applied to heat transfer structure with complex construction,which is thought to be solved by traditional design method.Both the Dirichlet boundary and Neumann boundary conditions in steady-state heat conduction problems were considered.A topology optimization mathematical model based on the variable density method was developed,and the optimality criterion method satisfying the KKT (Karush-Kuhn-Tucker) condition was presented.Numerical examples with different boundary conditions were illustrated to verify the suggested approach.And the technique for eliminating numerical unstability,such as the checkerboard phenomenon,was also discussed.An example of thin walled tube shows that the method is also adapted to the three-dimensional problems.