A novel hyperbolic-circular flexure hinge was presented. According to the Castigliano′s second theorem, the compliance calculations of the flexure hinge were derived. From the deduced equations, the effects of radius, minimum thickness and depth of cut on the hinge for flexibilities were deeply researched. Meanwhile, the finite element model of the flexible hinge was also built by adopting solid element, and then the simulations of different geometric parameters were obtained. Comparing simulations and analytical solutions explained that: the maximum error is below 8%, which verified the correctness of the equations. In addition, the comparisons on the flexibilities of flexure hinges with various shapes showed that: the hyperbolic-circular flexure hinge had better ability to rotate and higher sensitivity to load. Thus, the design of the new hyperbolic-circular flexure hinges in this paper is more suitable for support structure of Fast Steering Mirror and provides a theoretical basis for design and optimization of hybrid flexure hinges.