"Swimming Through Fear" is a typical example of a reading text from a Chinese university course book for students of English. This article first draws on three interconnected sources to analyse this text and understand its nature: genre study in Systemic Functional Linguistics; the generic structure of anecdotes (Salmaso, 2017); and the analytical strategy of Appraisal in narrative expounded by Macken-Horarik (2003a). The analysis shows how the Appraisal resources in "Swimming Through Fear" are deployed to construe the author's intended evaluation for its specific purpose as anecdote, with a "top-down and across" analysing procedure from the culture-related generic structure to the linguistic features (Gardner, 2017, p. 482). This article then applies a genre-based approach to teaching anecdotes in EFL classrooms. The aim of this project is to raise the awareness of genre study in EFL teaching to enhance students' reading ability and the essential role of the Appraisal system in realizing anecdotes as a distinctive instance of the narrative genre.