Recent years have witnessed the popularity of using two-stream convolutional neural networks for action recognition. However, existing two-stream convolutional neural network-based action recognition approaches are incapable of distinguishing some roughly similar actions in videos such as sneezing and yawning. To solve this problem, we propose a Multi-head Attention-based Two-stream EfficientNet (MAT-EffNet) for action recognition, which can take advantage of the efficient feature extraction of EfficientNet. The proposed network consists of two streams (i.e., a spatial stream and a temporal stream), which first extract the spatial and temporal features from consecutive frames by using EfficientNet. Then, a multi-head attention mechanism is utilized on the two streams to capture the key action information from the extracted features. The final prediction is obtained via a late average fusion, which averages the softmax score of spatial and temporal streams. The proposed MAT-EffNet can focus on the key action information at different frames and compute the attention multiple times, in parallel, to distinguish similar actions. We test the proposed network on the UCF101, HMDB51 and Kinetics-400 datasets. Experimental results show that the MAT-EffNet outperforms other state-of-the-art approaches for action recognition.