To improve the rotation accuracy of fast steering mirror(FSM) which is driven by PZT, the fillet triangle flexible support is investigated in this paper. First, the flexibility equations and rotation accuracy equations of the fillet triangle flexure hinge are deduced on the basis of the Castigliano’s second theorem. After that, the finite element models of a fillet triangle flexure hinge and a fillet triangle two-axis flexure support are established to analyze the simulation results. The simulation values of the flexibility and rotation accuracy are obtained. Comparing simulation results with analytical solutions, we can conclude that the maximum error is less than 8%, which verifies the accuracy of the equations. The rotation accuracy of the fillet triangle two-axis flexure support has increased 40% compared with the circular flexure support under the premise in flexibility. The study has significant values for industrial applications.