Peer assessment is the alternative assessment used by a teacher/ lecturer in assessing process and product in English language teaching and learning. The practice of peer assessment in higher education fosters graduate students more actively in the assessment process. This article aimed to explore graduate students' perceptions of the practice of peer assessment in an academic writing class conducted in the first semester of the English department graduate program at a University in Surakarta. This research was a case study, and the sampling technique in this research was purposive sampling, where 24 graduate students in academic writing class participated. A focused interview was conducted to explore graduate students' views on the practice of peer assessment for academic writing, which covered the feeling and challenges during peer assessment activity. The data were analyzed through the stages of examining, categorizing, tabulating, and recombining data. This study's result reveal that the peer assessment practice in academic writing class helps graduate students find the weaknesses in their writing that the they could not see by themselves. Feedback from peers during peer assessment practice completed the understanding of things the graduate students needed for revision. This research is expected to contribute to educational development by encouraging English writing lecturers' awareness to optimize peer assessment practice for assessing students writing.Keywords: peer-assessment, scientific writing, students’ perception