It is well known that the computational cost of classic topology optimization (TO) methods increases rapidly with the size of the design problem because of the high-dimensional numerical simulation required at each iteration. Recently, the technical route of replacing the TO process with artificial neural network (ANN) models has gained popularity. These ANN models, once trained, can rapidly produce an optimized design solution for a given design specification. However, the complex mapping relationship between design specifications and corresponding optimized structures presents challenges in the construction of neural networks with good generalizability. In this paper, we propose a new design framework that uses deep learning techniques to accelerate the TO process. Specifically, we present an efficient topology optimization (ETO) framework in which structure update at each iteration is conducted on a coarse scale and a structure mapping neural network (SMapNN) is constructed to map the updated coarse structure to its corresponding fine structure. As such, fine-scale numerical simulations are replaced by coarse-scale simulations, thereby greatly reducing the computational cost. In addition, fragmentation and padding strategies are used to improve the trainability and adaptability of SMapNN, leading to a better generalizability. The efficiency and accuracy of the proposed ETO framework are verified using both benchmark and complex design tasks. It has been shown that with the SMapNN, TO designs of millions of elements can be completed within a few minutes on a personal computer.