Evolutionary computation is a powerful tool for developing computer games. Back-propagation neural network(BPNN) was proved to be a universal approximator and genetic algorithm(GA) a global searcher. The game of Tic-Tac-Toe, also known as Naughts and Crosses, is often used as a test bed for testing new AI algorithms. We tried to recognize the strategic fitness of a finished Tic-Tac-Toe game when the parameters, such as a sequence of moves, its game depth and result, are provided. To implement this, we've constructed an evolutionary model using GA with back-propagation NNs(GANN). The experimental results revealed that GANN, in the very long training time, converges very slowly; however, performance of recognizing the strategic fitness does not meet we expected and, further, increase of the population size does not significantly contribute to the performance of GANN.