The composite predicate, such as have a look/rest/try, referred to as the “Have a N_Dev” structure in this article, has received a lot of attention in the previous studies. However, few studies have investigated its grammatical function and constructionalization features. This article, based on the discussion of the grammatical metonymic function of the structure, argues that this structure is a metaphor of two levels and that it manifests the basic features of construction as defined by Goldberg (2006) in that it has the abstract construction meaning and the function of construction fusion. Following that, the article analyses the degree of constructionalization and regularity of this structure from the dimensions of its schematicity, productivity, and compositionality. It is found that this structure has a high degree of schematicity and productivity and a low degree of compositionality.