We propose a novel feedforward neural network (FFNN)-based speech emotion recognition system built on three layers: A base layer where a set of speech features are evaluated and classified; a middle layer where a speech matrix is built based on the classification scores computed in the base layer; a top layer where an FFNN- and a rule-based classifier are used to analyze the speech matrix and output the predicted emotion. The system offers 80.75% accuracy for predicting the six basic emotions and surpasses other state-of-the-art methods when tested on emotion-stimulated utterances. The method is robust and the fastest in the literature, computing a stable prediction in less than 78 s and proving attractive for replacing questionnaire-based methods and for real-time use. A set of correlations between several speech features (intensity contour, speech rate, pause rate, and short-time energy) and the evaluated emotions is determined, which enhances previous similar studies that have not analyzed these speech features. Using these correlations to improve the system leads to a 6% increase in accuracy. The proposed system can be used to improve human–computer interfaces, in computer-mediated education systems, for accident prevention, and for predicting mental disorders and physical diseases.