In this paper, we develop the thinking extension education program for the gifted students of information and prove the validity and effectiveness of the proposed model by presenting the Tic-tac-toe problem as the practical example of the information-gifted students. This model consists of four phases which has the game tree as data structure and the search of game lee as control structure. And the search of game tree becomes the basis of the thinking extension education program. This model gives the help for students to learn representing the problem as tree structure and solving the problem of tree structure using the search method of game tree. The internal ability of the information-gifted for thinking extension of this education program contains the fluency, perceptiveness, originality, power of concentration, imaginative power, analyzing skills, pattern recognition, space sense, synthesizing, problem-solving.