The spacer grid set is a component in the nuclear fuel assembly. The set supports the fuel rods safely. Therefore, the spacer grid set should have sufficient strength for the external impact forces such as earthquake. The fretting wear occurs between the spring of the fuel rod and the spacer grid due to flow-induced vibration. Conceptual design of the spacer grid set is performed based on the Independence Axiom of axiomatic design. Two functional requirements are defined for the impact load and the fretting wear, and corresponding design parameters are selected. The overall flow of design is defined according to the application of axiomatic design. Design for the impact load is carried out by using nonlinear dynamic analysis to determine the length of the dimple. Topology optimization is carried out to determine a new configuration of the spring. The fretting wear is reduced by shape optimization using the homology theory. The deformation of a structure is called homologous if a given geometrical relationship holds before, during, and after the deformation. In the design to reduce the fretting wear, the deformed shape of the spring should be the same as that of the fuel rod. This condition is transformed to a function and considered as a constraint in the shape optimization process. The fretting wear is expected to be reduced due to the homology constraint. The objective function is minimizing the maximum stress to allow a slight plastic deformation. Shape optimization results are confirmed through nonlinear static analysis.