A method for the shape finding of a specific type of self-anchored suspension bridge whose main cable is three-dimensionally curved is proposed in this study. The method, referred to as the coordinate iteration method (CIM), is developed from the force equilibrium features of the rational arch axis for suspension cables modeled by truss-cable elements. By establishing the linear iterative equations in terms of unknown coordinates and updating the relation matrices iteratively, a trial profile of the three-dimensional cable-only system easily and stably converges to the target system. The CIM is then extended to the shape finding of the total bridge system with the aid of a specific numerical model proposed in this study referred to as the indiscrimination coordinate rod model (ICRM). This model is used to simulate the core deformation effects of the total bridge. The detailed procedure undertaken to establish a finite-element model of the equilibrium system for the finished dead load state based on CIM and ICRM is also presented. The precision and efficiency of the method are demonstrated through actual numerical examples.