Pun, an effective rhetorical device, is being widely used in advertising. The study of puns in advertisements has been so far focused on their grammatical structures, rhetorical features, pragmatic functions and aesthetic effects. Based on the Conceptual Integration Theory, this paper explaines the core part of cognitive process, namely input spaces, cross-space mapping, blended space, emergent structure as well as the whole function process by means of network diagrams of conceptual integration. Meanwhile, by displaying the necessary condition of punning-double contexts, it explores the meaning of puns in advertising. In the paper, the cognitive construction of puns in advertisements is analyzed and the dynamic perceptions are processed in terms of Conceptual Integration Theory, and the translation strategies of puns are discussed in terms of Delabastita's theory.