This study examines the optimum shape of a trolley, the driving device of the retractable membrane roof. The closed-type trolley was determined as the model of the study, and a trolley composed of cylindrical-shaped inner and outer holders was selected as the basic model. Based on this model, a cylindrical-based optimal trolley model was proposed. In the basic trolley model, steel was used for the outer holder, and steel, titanium, and aluminum were used for the inner holder. In each case, the most economical shape for the external load of the basic model was newly proposed through the topology optimization process, and the finite element analysis results of the proposed model were compared to define the durability and economics. Here, topology optimization analysis and finite element analysis used the commercial software ANSYS. As a result of optimization, the volume of the outer holder of the trolley was reduced by 58.2% and the volume of the inner holder was reduced by 25.0% compared to the basic model. In the case of stress, a stress increase of 43.2 to 79.2% occurred depending on the material of the inner holder, but it was found to be significantly lower than the yield strength, thereby ensuring safety.