This paper proposes a new type of flexure hinge: the sinc flexure hinge. A theoretical compliance and precision factor model of the sinc flexure hinge is developed based on the transfer matrix method. The finite element simulation is carried out using ANSYS Workbench. The error between the modeling and simulation results obtained is less than 7.0%. The influence of structural parameters on the compliance, precision factor, and compliance–precision ratio is analyzed. The results show that the compliance and precision are contradictory and that the minimum thickness has the most significant influence on performance. Compared with the other seven types of flexure hinges, the sinc flexure hinge delivers a good overall performance. Finally, a sinc flexure hinge is machined and its compliance is measured. The error between the experimental and theoretical values is less than 7.6%. Both the simulation and experimental results verify the effectiveness of the model.