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Few-shot classification tends to struggle when it needs to adapt to diverse domains. Due to the non-overlapping label space between domains, the performance of conventional domain adaptation is limited. Previous work tackles the problem in a transductive manner, by assuming access to the full set of test data, which is too restrictive for many real-world applications. In this paper, we set out to tackle this issue by introducing a inductive framework, DaFeC, to improve Domain adaptation performance for Few-shot classification via Clustering. We first build a representation extractor to derive features for unlabeled data from the target domain (no test data is necessary) and then group them with a cluster miner. The generated pseudo-labeled data and the labeled source-domain data are used as supervision to update the parameters of the few-shot classifier. In order to derive high-quality pseudo labels, we propose a Clustering Promotion Mechanism, to learn better features for the target domain via Similarity Entropy Minimization and Adversarial Distribution Alignment, which are combined with a Cosine Annealing Strategy. Experiments are performed on the FewRel 2.0 dataset. Our approach outperforms previous work with absolute gains (in classification accuracy) of 4.95%, 9.55%, 3.99% and 11.62%, respectively, under four few-shot settings.