Many researchers have recently been interested in the Genre-based analysis of the manipulation of academic writing language such as the rhetorical moves of the thesis abstract section. Genre-based analysis of rhetorical move structure provides a keen eye on the effective organizational and functional aspects of abstract components. These rhetorical move structures have often been overlooked or written differently by different writers, especially in the Iraqi context, that is, M.A linguistics thesis abstract section written by Iraqi postgraduate students. A few studies on rhetorical move structures have been conducted in the Iraqi M A linguistics university context, hence more studies are required. To this end, thirty M.A linguistics thesis abstracts have been purposively selected from three Iraqi public universities representing different parts of Iraq. Therefore, the current study is a genre-based analysis of the rhetorical move structure of Iraqi Post-Graduate Students. Swales ( 2004) model has been adopted to qualitatively analyze the rhetorical move structures of the thesis abstract. The findings revealed that there were few researchers following the structure of (Move1, Move2, and Move3). Also, there was a misuse of M2. Finally, the study implicates further application of genre-based analysis in both EFL and ESL contexts.