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The aim of any genre of writing is an important aspect that needs to be considered by writers. However, keeping the aim of the writing is not enough. As writing is meant to be read by readers, a writer needs to consider who their intended readers are. In line with this idea, the objective of this study is to investigate the undergraduate students ways of persuading readers in their argumentative writing. This study uses three kinds of cognitive consideration in writing argumentative text (Connor, 1991) that involve (a) readers domain knowledge and text structure; (b) readers attitude toward the subject; (c) textual cues; and (d) reasoning. The data of this study is gathered by using elicitation technique asking the subjects, the 8th semester of undergraduate students, to write under predetermined topic Social media should be banned with three intended readers, they are: Junior High School, Senior High School, and Undergraduate students. This study reveals that the subjects in EFL context only have two kinds of cognitive consideration in writing argumentative text, they are: (a) readers domain knowledge and text structure; and (b) reasoning. These kinds of consideration are applied across all intended readers. It means that the subjects do not have specific cognitive considerations for specific readers. Keywords: cognitive, argumentative, writing, persuasive