Transformer has emerged in speech emotion recognition (SER) at present. However, its equal patch division not only damages frequency information but also ignores local emotion correlations across frames, which are key cues to represent emotion. To handle the issue, we propose a Local to Global Feature Aggregation learning (LGFA) for SER, which can aggregate longterm emotion correlations at different scales both inside frames and segments with entire frequency information to enhance the emotion discrimination of utterance-level speech features. For this purpose, we nest a Frame Transformer inside a Segment Transformer. Firstly, Frame Transformer is designed to excavate local emotion correlations between frames for frame embeddings. Then, the frame embeddings and their corresponding segment features are aggregated as different-level complements to be fed into Segment Transformer for learning utterance-level global emotion features. Experimental results show that the performance of LGFA is superior to the state-of-the-art methods.