The networking method of Bennett linkages is investigated, and a deployable parabolic cylindrical antenna is constructed based on the network. The units are parallel in one direction and have an included angle in the vertical direction in the network. The mobility of the mechanical network is analyzed through screw theory. A method of constructing parabolic cylindrical antennas is proposed. The parameters of units in the network are analyzed. The parabolic cylindrical antenna can be folded completely and can be deployed to the predetermined profile.