We introduce a new neural network for 2D pattern classification. The new neural network, termed as localized receptive field neural network (RFNet), consists of a receptive field layer for 2D feature extraction, followed by one or more 1D feedforward layers for feature classification. All synaptic weights and biases in the network are automatically determined through supervised training. In this paper, we derive five different training methods for the RFNet, namely gradient descent, gradient descent with momentum, resilient backpropagation, Polak-Ribiere conjugate gradient, and Levenberg-Marquadrt algorithm. We apply the RFNet to classify face and nonface patterns, and study the performances of the training algorithms and the RFNet classifier in this context.