The multi-vertex rigid origami mechanism is a spatial mechanism that can be folded and expanded. The three-vertex rigid origami mechanism is a form of multi-vertex. Aiming at the foldability of the three-vertex rigid origami mechanism， a method based on screw theory in kinematics is proposed to analyze the foldability of this type of mechanism. The kinematics of the three-vertex rigid origami mechanism is equivalent to a double-branched closed-loop 6R mechanism， and the velocity equation of the closed-loop mechanism is established. The linear correlation between the motion screws of the kinematic pairs is judged to determine the movability of the motion equivalent mechanism. Based on the Grassmann line geometry principle， the dimensions of different types of rigid origami mechanisms were determined， and the linear relation of motion screws of the rigid origami mechanism was verified. The synthetical method of kinematic equivalence and linear correlation analysis of motion screws of three-vertex rigid origami mechanism can realize the judgment of foldability of the three-vertex rigid origami mechanism from the perspective of kinematic analysis， and can be extended to the research of other multi-vertex rigid origami mechanism.