Using standard idea from differential topology, this paper presents a detailed analysis of the topology structure of configuration space of general close-chain mechanisms. A diffeomorphic theorem on configuration space is proposed and its proof is given by using the Morse theory and critical value theory. Relations between the configuration space singularity and topology structure are described, which show that the topology structure of configuration space of close-chain mechanisms will change at the configuration singularity. Finally, the topology structure of a four-bar planar mechanism is analyzed, as an example, to verify the proposed theorem.