Abstract: The special parts of structures are always required to be geometric stable on output displacements under different loadings in many engineering cases. Introduction of the adjustable compensation displacements in the special region of structures is the effective technique. In the scope of the linearly elasticity and small deformation, the purpose of this paper is to study the topology optimization of structures with the geometric stability in the given region through the lowest compensation cost. The objective of the present optimization model is to obtain the maximum sti ness of structures with the stable ideal displacement responses of structural given region. There are two types of design variables in the model which are the structural topology variables and the compensation displacement variables. These two types of variables are coupled through the two-level search method. The adjoint method is performed to compute the sensitivities of the objective function with respect to the two types of variables respectively. The results show that the present optimization formulation can realize the objective of shape control of structures through the low controlling cost.