Automatic emotion recognition from speech, which is an important and challenging task in the field of affective computing, heavily relies on the effectiveness of the speech features for classification. Previous approaches to emotion recognition have mostly focused on the extraction of carefully hand-crafted features. How to model spatio-temporal dynamics for speech emotion recognition effectively is still under active investigation. In this paper, we propose a method to tackle the problem of emotional relevant feature extraction from speech by leveraging Attention-based Bidirectional Long Short-Term Memory Recurrent Neural Networks with fully convolutional networks in order to automatically learn the best spatio-temporal representations of speech signals. The learned high-level features are then fed into a deep neural network (DNN) to predict the final emotion. The experimental results on the Chinese Natural Audio-Visual Emotion Database (CHEAVD) and the Interactive Emotional Dyadic Motion Capture (IEMOCAP) corpora show that our method provides more accurate predictions compared with other existing emotion recognition algorithms.