Selecting an appropriate recognition method is crucial in speech emotion recognition applications. However, the current methods do not consider the relationship between emotions. Thus, in this study, a speech emotion recognition system based on the fuzzy cognitive map (FCM) approach is constructed. Moreover, a new FCM learning algorithm for speech emotion recognition is proposed. This algorithm includes the use of the pleasure-arousal-dominance emotion scale to calculate the weights between emotions and certain mathematical derivations to determine the network structure. The proposed algorithm can handle a large number of concepts, whereas a typical FCM can handle only relatively simple networks (maps). Different acoustic features, including fundamental speech features and a new spectral feature, are extracted to evaluate the performance of the proposed method. Three experiments are conducted in this paper, namely, single feature experiment, feature combination experiment, and comparison between the proposed algorithm and typical networks. All experiments are performed on TYUT2.0 and EMO-DB databases. Results of the feature combination experiments show that the recognition rates of the combination features are 10%-20% better than those of single features. The proposed FCM learning algorithm generates 5%-20% performance improvement compared with traditional classification networks.