Recently, the hardware realizations of the neural networks for specially-purposed-use have been in focus. In this paper, two kinds of networks, a two-layer network and the Boltzmann machine, using the switched-capacitor circuit are proposed. The variable synaptic weights of neural circuit are realized by through the programmable capacitor array (PCA) in the switched-capacitor variable-coefficients multiplier. As a result, the recognition system of the handwritten character using a two-layer neural network is constructed by the discrete electronic elements and its desirable effects are shown by the experimental results. The stochastic operation in the processing element (PE) of the Boltzmann machine is realized by using the generation of noise voltage with the random number and is also confirmed by teh experimental results using the discrete electronic elements. Furthermore, the operations of the PE have been also confirmed by using the simulation of Traveling-Salesman Problem.