A curved slotted Geneva mechanism can eliminate the adversely infinite angular jerks of the Geneva wheel and might reduce the peak angular acceleration of the Geneva wheel by using a proper indexing motion program. In the literature, the cycloidal, fifth-order polynomial and modified sine indexing motion programs are frequently used for curved slotted Geneva mechanisms. To achieve the better kinematic performance of the curved slotted Geneva wheel than that obtained using the above-mentioned indexing motion programs, a new indexing motion program based on the Hermite interpolating polynomial is proposed for an optimum design with the goals of minimizing the peak angular acceleration and eliminating the adversely infinite angular jerks. The domain of the indexing position function is divided into several segments. Each segment is termed an element, and both ends of each segment are termed nodes. The nodal values of the indexing position function and its derivatives are used as design variables. The position function for each element can be described using the Hermite interpolating polynomial and the design variables. The reason behind the use of the Hermite interpolating polynomial is that the design variables have the clear physical meanings. The four-level Hermite interpolating polynomial is used and two elements are sufficient to obtain the optimum results. In addition, the constraint regarding the radius of curvature of the profile of the inner slot is proposed to prevent sharp curvature of the profile of the inner slot. The findings show that there is a decline in the peak acceleration of the Geneva wheel with six curved slots for the optimum results obtained using the proposed indexing motion program by 33.4% and 24.3%, respectively, as compared with the cycloidal and modified sine indexing motion programs.