As a powerful design tool, topology optimization methods have been widely studied for the optimizations of practical structures. Cast iron, concrete, porous materials, and other materials, which have bi-modulus characteristics with unequal tensile and compressive moduli, are often used in practical engineering. Therefore, it is of great theoretical and engineering significance to consider the bi-modulus material properties for structural topological optimization design. The non-smoothness bi-modulus properties would bring many difficulties for the numerical analyses during topology optimization process, such as the non-smoothness, and the complexity of the calculation of enormous adjoint equations. Aiming at the above problems, this paper constructs an approximate smooth elastic modulus matrix of bi-modulus materials, deduces an explicit sensitivity equation considering the nonlinearity of materials, and develops an efficient topology optimization method for bi-modulus materials. Through the co-simulation optimization of MATLAB and ABAQUS, the structural topology optimization of bi-modulus material structures is realized, and typical numerical examples are given. The method proposed in this paper effectively reduces the difficulty of topology optimization analysis of bi-modulus materials, and lays a foundation for the future topology optimization design of bi-modulus materials in problems such as stress constraint, structural buckling, and thermal-mechanical coupling.