The reconfigurable mechanisms can satisfy the requirements of changing environments, working conditions, and tasks on the function and performance of the mechanism and can be applied to machine tool manufacturing, space detection, etc. Inspired by the single-vertex fivefold origami pattern, a new reconfigurable parallel mechanism is proposed in this paper, which has special singular positions and stable motion due to replicating the stabilizing kinematic properties of origami. Through analyzing the topologic change of the folding process of the pattern and treating it as a reconfigurable joint, a new reconfigurable parallel mechanism with 3, 4, 5, or 6 degrees of freedom is obtained. Then, the kinematics solution, workspace, and singularity of the mechanism are calculated. The results indicate that the singular configuration of the origami-derived reconfigurable parallel mechanism is mainly located in a special plane, and the scope of the workspace is still large after the configuration change. The mechanism has the potential to adapt to multiple tasks and working conditions through the conversion among different configurations by folding reconfigurable joints on the branch chain.