In a previous study about a combinatorial optimization problem solver using neural networks, since the Hopfield method, convergence to the optimum solution sooner and with more certainty is regarded as important. Namely, only static states are considered as the information. However, from a biological point of view, dynamical systems have attracted attention recently. Therefore, we propose a "dynamical" combinatorial optimization problem solver using hysteresis neural networks. In this paper, the proposed system is evaluated by the N-Queen problem.