This paper tackles the Few-shot Semantic Segmentation (FSS) task with focus on learning the feature extractor. Somehow the feature extractor has been overlooked by recent state-of-the-art methods, which directly use a deep model pretrained on ImageNet for feature extraction (without further fine-tuning). Under this background, we think the FSS feature extractor deserves exploration and observe the heterogeneity (i.e., the intra-class diversity in the raw images) as a critical challenge hindering the intra-class feature compactness. The heterogeneity has three levels from coarse to fine: 1) Sample-level: the inevitable distribution gap between the support and query images makes them heterogeneous from each other. 2) Region-level: the background in FSS actually contains multiple regions with different semantics. 3) Patch-level: some neighboring patches belonging to a same class may appear quite different from each other. Motivated by these observations, we propose a feature extractor with Multi-level Heterogeneity Suppressing (MuHS). MuHS leverages the attention mechanism in transformer backbone to effectively suppress all these three-level heterogeneity. Concretely, MuHS reinforces the attention / interaction between different samples (query and support), different regions and neighboring patches by constructing cross-sample attention, cross-region interaction and a novel masked image segmentation (inspired by the recent masked image modeling), respectively. We empirically show that 1) MuHS brings consistent improvement for various FSS heads and 2) using a simple linear classification head, MuHS sets new states of the art on multiple FSS datasets, validating the importance of FSS feature learning.