The Convex Linearization method (CONLIN), that is a dual optimizer based on the convex approximation concepts, is often used to solve the structural optimization problem, recently. The CONLIN optimizer has many benefits, for example, the handling of constraint conditions is easy as well as the SLP method, and the performance of convergence is excellent as well as the optimality criteria method (OC). In this paper, the CONLIN optimizer is applied to the topology optimization problem of three-dimensional structures. The density approach is used to obtain the optimum topology, and the filtering method proposed by the author is used to obtain the clearer topology. In the optimization problem, the total volume and the value of the gravity function which is used for the filtering are constrained. The validity of the CONLIN optimizer are clarified by comparing with the OC method. Some examples of bridge design are shown to demonstrate the effectiveness of the CONLIN optimizer for the topology optimization analysis.