Emotion recognition based on electroencephalography (EEG) is a significant task in the brain-computer interface field. Recently, many deep learning-based emotion recognition methods are demonstrated to outperform traditional methods. However, it remains challenging to extract discriminative features for EEG emotion recognition, and most methods ignore useful information in channel and time. This paper proposes an attention-based convolutional recurrent neural network (ACRNN) to extract more discriminative features from EEG signals and improve the accuracy of emotion recognition. First, the proposed ACRNN adopts a channel-wise attention mechanism to adaptively assign the weights of different channels, and a CNN is employed to extract the spatial information of encoded EEG signals. Then, to explore the temporal information of EEG signals, extended self-attention is integrated into an RNN to recode the importance based on intrinsic similarity in EEG signals. We conducted extensive experiments on the DEAP and DREAMER databases. The experimental results demonstrate that the proposed ACRNN outperforms state-of-the-art methods.