Fine-grained visual classification (FGVC) is much more challenging than traditional classification tasks due to the inherently subtle intra-class object variations. Recent works mainly tackle this problem by focusing on how to locate the most discriminative parts, more complementary parts, and parts of various granularities. However, less effort has been placed to which granularities are the most discriminative and how to fuse information cross multi-granularity. In this work, we propose a novel framework for fine-grained visual classification to tackle these problems. In particular, we propose: (i) a progressive training strategy that effectively fuses features from different granularities, and (ii) a random jigsaw patch generator that encourages the network to learn features at specific granularities. We obtain state-of-the-art performances on several standard FGVC benchmark datasets, where the proposed method consistently outperforms existing methods or delivers competitive results. The code will be available at https://github.com/PRIS-CV/PMG-Progressive-Multi-Granularity-Training.