A new type of flexible hinges was proposed, which were double sided circular- parabolic hinges. The theoretical structure model of the hinges was established. The Castigliano′s second theorem and calculus theory were used to calculate the main performance indexes that were compliance and rotational accuracy of the hinges. The theoretical calculation and finite element analysis of the compliance and rotational accuracy were carried out. At the same time, the structural parameters that affected the hinges′ performance were studied. The results show that the theoretical values of compliance and rotational accuracy were better than those of the finite element analysis, and the consistency was greater than 92%. And the minimum cutting thickness t had the greatest influence on the change of hinges′ compliance. As a new type of hinge, compared with other flexible hinges, the circular-parabolic hinges combined the advantages of straight circular hinges and parabolic hinges. At that time, the hinges had stronger rotation performance and weaker load sensitivity, and the thermal adaptability was stronger. The design of the circular-parabolic hinges provids guidance for the design of the support structure including using in the space environment.