A new methodology for understanding the construction of dodecahedral links has been developed on the basis of dodecahedron structure and DNA circles. Knots are interlaced cyclic structures while links are at least two cyclic structures mutually interlaced. A new series of DNA dodecahedral links have been given. By assigning an orientation to the links we analyze the knot invariant of these dodecahedral links. This study provides further insight into the molecular design, as well as theoretical characterization of the DNA catenanes.