Dots and Boxes game is a familiar pencil and paper game for two players [1]. This paper proposed a new method to represent the chessboard of Dots-and-Boxes, which can be used more conveniently and quickly to recognize and evaluate any situations of the chessboard formed in the process of playing game than other representation methods. In the 4^th machine gambling tournament took in 2010, the realized Dots-and-Boxes system gained the fifth best, which indicates the feasibility of the proposed chessboard representing method and the validity of the Dots-and-Boxes system.