An optimization approach for black-and-white and hinge-removal topology designs is studied. To achieve this motive, an optimal topology allowing grey boundaries is found firstly. When a suitable design has been obtained, this solution is then used as a starting point for the follow-up optimization with the goal to free unfavorable intermediate elements. For this purpose, an updated optimality criterion in which a threshold factor is introduced to gradually suppress elements with low density is proposed. The typical optimality method and new technique proposed are applied to the design procedure sequentially. Besides, to circumvent the one-point hinge connection problem producing in the process of freeing intermediate elements, a hinge-removal strategy is also proposed. During the optimization, the binary constraints on design variables are relaxed based on the scheme of solid isotropic material with penalization. Meanwhile, the mesh-independency filter is employed to ensure the existence of a solution and remove well-known checkerboards. In this way, a solution that has few intermediate elements and is free of one-point hinge connections is obtained. Finally, different numerical examples including the compliance minimization, compliant mechanisms and vibration problems demonstrate the validity of the proposed approach.