This paper presents a simple continuous analog hardware realization of the Random Neural Network (RNN) model. The proposed circuit uses the general principles resulting from the understanding of the basic properties of the firing neuron. The circuit for the neuron model consists only of operational amplifiers, transistors, and resistors, which makes it candidate for VLSI implementation of random neural networks with feedforward or recurrent structures. Although the literature is rich with various methods for implementing the different neural network structures, the proposed implementation is very simple and can be built using discrete integrated circuits for problems that need a small number of neurons. A software package, RNNSIM, has been dev eloped to train the RNN model and supply the network parameters, which can be mapped to the hardware structure. As an assessment on the proposed circuit, a simple neural network mapping function has been designed and simulated using PSpice.