Query expansion (QE) is a well known technique to improve retrieval effectiveness, which expands original queries with extra terms that are predicted to be relevant. A recent trend in the literature is Supervised Query Expansion(SQE), where supervised learning is introduced to better select expansion terms. However, an important but neglected issue for SQE is its efficiency, as applying SQE in retrieval can be much more time-consuming than applying Unsupervised Query Expansion (UQE) algorithms. In this paper, we point out that the cost of SQE mainly comes from term feature extraction, and propose a Two-stage Feature Selection framework (TFS) to address this problem. The first stage is adaptive expansion decision, which determines if a query is suitable for SQE or not. For unsuitable queries, SQE is skipped and no term features are extracted at all, which reduces the most time cost. For those suitable queries, the second stage is cost constrained feature selection, which chooses a subset of effective yet inexpensive features for supervised learning. Extensive experiments on four corpora (including three academic and one industry corpus) show that our TFS framework can substantially reduce the time cost for SQE, while maintaining its effectiveness.