This paper presents a novel deployable mechanism for approximating the parabolic cylindrical surface. The proposed mechanism, which can deploy and fold synchronously in the radial and axial directions, is constructed by double four-bar linkages and scissor linkages. In the fully deployed configuration, the mechanism can approximate a cylindrical surface. It can also be folded compactly into a bundle. The radial and axial deployable mechanisms are described and their position kinematics are solved. A synchronous mechanism is designed to ensure the synchronous movement of the radial and axial mechanisms. Geometric parameters of the mechanism for approximating a given parabolic cylindrical surface are obtained. The magnification ratio of the designed mechanism is calculated. The best choice of actuator is determined through static-load analysis.