In this paper we present a Linear Vector Quantization (LVQ) neural network approach to estimate Direction of Arrivals (DOA) of narrowband sources. It is shown that appropriately trained LVQ networks along with a specific postprocessing scheme can successfully be used for DOA estimation purposes. We take advantage of the execution speed of LVQ algorithm to accurately classify an incoming signal on a uniform linear antenna array with unknown source location in a reference class chosen among a set of predefined classes. DOA estimation is made through a multistage process that avoids complex and time-consuming eigenvalue decomposition (EVD) calculations used in the classical subspace based estimation methods, MUSIC and ESPRIT. An accurate DOA estimation method that can accommodate high rates of neural networks classification errors and suitable for real-time applications is demonstrated with system performances that are in good agreement with high-resolution subspace based models.