Idioms are peculiar linguistic constructions that impose great challenges for representing the semantics of language, especially in current prevailing end-to-end neural models, which assume that the semantics of a phrase or sentence can be literally composed from its constitutive words. In this paper, we propose an idiom-aware distributed semantic model to build representation of sentences on the basis of understanding their contained idioms. Our models are grounded in the literal-first psycholinguistic hypothesis, which can adaptively learn semantic compositionality of a phrase literally or idiomatically. To better evaluate our models, we also construct an idiom-enriched sentiment classification dataset with considerable scale and abundant peculiarities of idioms. The qualitative and quantitative experimental analyses demonstrate the efficacy of our models.