Accurately recognizing emotion from speech is a necessary yet challenging task due to the variability in speech and emotion. In this paper, a novel method combined self-attention mechanism and multi-scale fusion framework is proposed for multi-modal SER by using speech and text information. A self-attentional bidirectional contextual LSTM (bc-LSTM) is proposed to learn the context-sensitive dependences from speech. Specifically, the BLSTM layer is applied to learn long-term dependencies and utterance-level contextual information and the multi-head self-attention layer makes the model focus on the features that are most related to the emotions. A self-attentional multi-channel CNN (MCNN), which takes advantage of static and dynamic channels, is applied for learning general and thematic features from text. Finally, a multi-scale fusion strategy, including feature-level fusion and decision-level fusion, is applied to improve the overall performance. Experimental results on the benchmark dataset IEMOCAP demonstrate that our method gains an absolute improvement of 1.48% and 3.00% over state-of-the-art strategies in terms of weighted accuracy (WA) and unweighted accuracy (UA), respectively.