To broaden the methods of configuration synthesis, this study proposes a new method for configuration synthesis and screening of multiple closed-loop unit tandem mechanisms. Firstly, some closed-loop configurations are taken as basic units, and the closed-loop basic units are synthesized in series under the condition of considering the basic unit types, contacts, and input and output relationships. Secondly, the connectivity of the mechanism is obtained by weighting the adjacency matrix, and the entropy weight method is used for the first time to establish a comprehensive evaluation index coefficient to assess the quality of the mechanism. Then, an improved simulated annealing-greedy algorithm is proposed and an algorithm software screening platform is built to screen mechanisms. Finally, the multi-fingered grasper is used as design case to verify the practicality of the proposed configuration synthesis and screening method. This study can provide a reference for theoretical research on the configuration synthesis and screening methods of multiple closed-loop unit tandem mechanisms.