A graph in which every vertex has the same valency or degree is known as a regular graph. The double graph D(G) of a regular graph is constructed by duplicating each vertex and connecting the corresponding duplicates if the original vertices are adjacent. This method creates a motivating and complex graph structure, raising questions about the domination properties of D(G).  In this paper we focus on the domination of double graph of some regular graphs which is constructed using an algorithm. The domination number γ of connected 2-regular graph on n nodes were found. Further the domination number γ of regular graphs on even and odd orders are determined.