To meet the requirements of high flexibility, high stiffness, and large working range of space debris cleaning technology, a foldable composite space capture mechanism is proposed based on the finite screw theory in this paper. The degree of freedom of the mechanism is analyzed by using the screw theory and its degree of freedom is obtained. The closed-loop vector method and DH method are used to analyze the kinematics of the mechanism, and the position solution of the mechanism is derived. The analytical expressions of velocity and acceleration solutions are obtained by differential calculation. According to the analysis of numerical example, the kinematic model of the mechanism is built in the simulation environment, and the simulation experiment is carried out for the motion trajectory of the mechanism. The correctness of theoretical analysis solution and method is proved by contrasting and analyzing motion trajectory, and it is verified that the space capture mechanism uses the foldable property to form large workspace to complete the capture of the target.