Multimodal emotion recognition is a challenging task in emotion computing as it is quite difficult to extract discriminative features to identify the subtle differences in human emotions with abstract concept and multiple expressions. Moreover, how to fully utilize both audio and visual information is still an open problem. In this paper, we propose a novel multimodal fusion attention network for audio-visual emotion recognition based on adaptive and multi-level factorized bilinear pooling (FBP). First, for the audio stream, a fully convolutional network (FCN) equipped with 1-D attention mechanism and local response normalization is designed for speech emotion recognition. Next, a global FBP (G-FBP) approach is presented to perform audio-visual information fusion by integrating selfattention based video stream with the proposed audio stream. To improve G-FBP, an adaptive strategy (AG-FBP) to dynamically calculate the fusion weight of two modalities is devised based on the emotion-related representation vectors from the attention mechanism of respective modalities. Finally, to fully utilize the local emotion information, adaptive and multi-level FBP (AMFBP) is introduced by combining both global-trunk and intratrunk data in one recording on top of AG-FBP. Tested on the IEMOCAP corpus for speech emotion recognition with only audio stream, the new FCN method outperforms the state-ofthe-art results with an accuracy of 71.40%. Moreover, validated on the AFEW database of EmotiW2019 sub-challenge and the IEMOCAP corpus for audio-visual emotion recognition, the proposed AM-FBP approach achieves the best accuracy of 63.09% and 75.49% respectively on the test set.