Speech emotion recognition plays a crucial role in human-machine interaction systems. Recently various optimized Transformers have been successfully applied to speech emotion recognition. However, the existing Transformer architectures focus more on global information and require large computation. On the other hand, abundant speech emotional representations exist locally on different parts of the input speech. To tackle these problems, we propose a Multi-Scale TRansfomer (MSTR) for speech emotion recognition. It comprises of three main components: (1) a multi-scale temporal feature operator, (2) a fractal self-attention module, and (3) a scale mixer module. These three components can effectively enhance the transformer's ability to learn multi-scale local emotion representations. Experimental results demonstrate that the proposed MSTR model significantly outperforms a vanilla Transformer and other state-of-the-art methods across three speech emotion datasets: IEMOCAP, MELD and, CREMAD. In addition, it can greatly reduce the computational cost.