The uncertainties in real structures usually lead to variations in their dynamic responses. In order to reduce the likelihood of unexpected failures in structures, it is necessary to reduce the response variations. Among various design manipulations, the modification of surface geometry could be a viable option to achieve performance robustness against uncertainties. However, such design modification is difficult to achieve based on conventional finite element methods, primarily due to the inevitable discrepancy between the conventional finite element mesh and the corresponding surface geometry. This issue may become even more severe in design optimization, as an optimized mesh based on conventional finite element analysis may yield nonsmooth surface geometry. In this research, we adopt the nonuniform rational B-splines (NURBS) finite element method to facilitate the robust design optimization (RDO), where the fundamental advantage is that the NURBS finite element mesh is conformal to the underlying NURBS geometry. Furthermore, this conformal feature ensures that, upon finite element-based optimization, the resulting surface geometry is smooth. Taking advantage of that both the uncertainties and the design modifications are small, we formulate a sensitivity-based algorithm to rapidly evaluate the response variations. Based on the direct relation between the response variations and design parameters, the optimal surface geometry that yields the minimal response variation can be identified. Systematic case analyses are carried out to validate the effectiveness and efficiency of the proposed approach.