The cooling stage greatly affects the product quality in the injection molding process. The cooling system that minimizes temperature variance in the product surface will improve the quality and the productivity of products. The cooling circuit optimization problem that was once solved by a response surface method with 4 design variables. It took too much time for the optimization as an industrial design tool. It is desirable to reduce the optimization time. Therefore, we tried the back-propagation algorithm of artificial neural network(BPN) to find an optimum solution in the cooling circuit design in this research. We tried various ways to select training points for the BPN. The same optimum solution was obtained by applying the BPN with reduced number of training points by the fractional factorial design.