To realize the flexural support for optical elements in a precision optical instrument, a Cartwheel bi-axial flexural hinge composed by filleted short beams was proposed. The dimensionless design graph method for the design of the spatial flexural hinge was presented. First, the parametric finite element analysis on the Cartwheel bi-axial flexural hinge was performed, and then a polynomial fitting was carried out according to the analysis results to establish the dimensionless design graph for the mechanical characteristics of the flexural hinge, such as rotational stiffness and maximum stress. A practical design by the dimensionless graph method was performed to satisfy the supporting demand of an optical instrument, and the finite element analysis was used to verify it also. Finally, an optical test platform was established, and the rotational stiffness of the design was measured. Obtained results show that the maximum relative error of the rotational stiffness between analysis result, test result and design result is 10.1%. In conclusion, by using the dimensionless design graph as a design tool, a designer can determine the optimal geometry rapidly and correctly of the Cartwheel bi-axial flexural hinge based upon its demands for the stiffness, rotation angle, maximum stress and the weight. This paper can provide reference for the application of the Cartwheel bi-axial flexural hinge in precision optical instruments.