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In this paper, implementing the table tennis game by robot arm with forward-backward neural network has been investigated. The main contributions have been made as the followings, (1) Based on 2-dimensions (2-D), both ideal model and improved model have been developed, creating a Ping-pong game by employing Visual C++. The example provide by this paper has shown that the two new model operate very well. (2) The 2-D approach for the game has been proposed and the calculation formulas of this approach have been strictly proofed by employing the small amplitude disturbed theory. (3) A novel 3-D approach has also been put up forwarded. By using 3-D approach, one can implement the game in 3 dimensions; it acts as a real game. Finally, the proposed 2-D and 3-D approaches are not only used in the Ping-pong game, can also be exploited to a motion target tracking such as a Ballistics Missile Defense System.