In this paper, we propose a method to design a neural network (NN) by using a genetic algorithm (GA) and simulated annealing (SA). In addition, in order to demonstrate the effectiveness of the proposed scheme, we apply the proposed scheme to a coin recognition example. In general, as a problem becomes complex and large-scale, the number of operations increases and hardware implementation to real systems (coin recognition machines) using NNs becomes difficult. Therefore, we propose the method, which makes a small-sized NN system to achieve a cost reduction and to simplify hardware implementation to the real machines. A cheap scanner took the coin images used in this paper. Then they are not perfect, but a part of the coin image could be used in computer simulations. Input signals, which are Fourier spectra, are learned by a three-layered NN. The inputs to NN are selected by using GA with SA to make a small-sized NN. Simulation results show that the proposed scheme is effective to find a small number of input signals for coin recognition.