The present application provides a multi-motion-platform parallel robot and a method of constructing the same. The parallel robot comprises a symmetrical basic parallel mechanism and one or more symmetrical branch parallel mechanism. The basic parallel mechanism comprises a symmetrical basic foundation platform, a symmetrical basic motion platform, and symmetrical main branched-chains. The branch parallel mechanism comprises a symmetrical branch foundation platform, a symmetrical branch motion platform, and symmetrical branch branched-chains. The basic parallel mechanism and the branch parallel mechanism are connected by means of a multiple-output motion pair having symmetrical output ends, and share one set of driving pairs and drive and control devices. The multi-motion-platform parallel robot and it's method of construction can be used for various industrial robots, three-dimensional profile modeling and scaling robots and walking robots, and have the advantages of having a simple structure, being easy to standardize, having a high production efficiency, and the like.