To enhance fuel safety and to achieve a power uprating, a new concept PWR (Pressurized Water Reactor) fuel, which is called a dual cooled fuel rod, has been studied since 2007. Although there are some challenging problems about each mechanical component, fuel rod supporting structures are especially dealt within this paper. In the dual-cooled annular fuel rod, an inner flow passage as well as an outer one is used not only to enhance the fuel safety but to achieve a power uprating through the decreasing fuel center temperature and increasing the heat transfer area between fuel and coolant. As a result, the diameter of dual-cooled fuel rods becomes 1.6 times bigger than a conventional solid fuel rod and the gap between the annular fuel and the spacer grid’s straps is narrowed. This is a current key issue of fuel rod supports. To accommodate the narrowed gap, spacer grids, such as the cantilever type, hemi-sphere type, circular insertion type, etc., were suggested. For some of these configurations, patents have been applied. The grid springs in a spacer grid play the role of holding the fuel rods in an appropriate position and preventing fuel rods from dropping during normal reactor operation. In the case of the dual cooled fuel rod, the total mass is increased. So, the stiffness of a grid spring has to be increased more than that of a conventional grid spring. However, if the stiffnesses of springs are increased too much, fuel rods can bend due to the prohibition of their axial slip. So, it is necessary to design an appropriate stiffness. In this paper, the minimum spring force to prevent dual-cooled fuel rods from dropping during normal reactor operation is calculated. The spring characteristics of a cantilever type and a hemi-sphere type are predicted. A finite element analysis is carried out by using the commercial code ABAQUS. The analysis results are verified by experiments. Finally, it is checked whether the property of the suggested springs satisfies the minimum required spring force. Based on the obtained results, a kind of spacer grid candidate for dual cooled fuel rods, i.e. a spacer grid with hybrid supports is suggested.