Recently, large multimodal models (LMMs) have achieved significant advancements. When dealing with high-resolution images, dominant LMMs typically divide them into multiple local images and a global image, leading to a large number of visual tokens. In this work, we introduce AVG-LLaVA, an LMM that can adaptively select the appropriate visual granularity based on the input image and instruction. Specifically, we first apply the multiple pooling layers to obtain visual tokens at different granularities. Then we propose a visual granularity router, which includes a Transformer layer, an MLP layer, and a voter layer, used to select the appropriate visual granularity based on the image and instruction. Furthermore, we put forward RGLF, a novel training paradigm that aims at aligning the granularity predicted by the router with the preferences of the LMM, without the need for additional manually annotated data. Extensive experiments and analysis show that AVG-LLaVA achieves superior performance across 11 benchmarks, as well as significantly reduces the number of visual tokens and speeds up inference (e.g., an 85.3% reduction in visual tokens and a 2.53$\times$ increase in inference speed on the AI2D benchmark).