The aim of the present study was to determine the effect of a collaborative writing programme through the Google Docs writing tool on the production of argumentative discourse within the framework of Modern Greek Language teaching. The participants were 23 pupils in Year 5 who received a six-month period teaching intervention (two hours per week) that included collaborative writing activities of argumentative discourse. Prior to the beginning, and following the end of the programme the performance of all participants on argumentative discourse writing skills was evaluated with a 13-criteria Rubric scale. The results of the paired-sample t-tests showed a statistically significant difference between pre- and post tests in the majority of the criteria and the total scores of the rubric. It is therefore concluded that, the use of a Web platform may positively contribute towards the enhancement of argumentative discourse writing skills of pupils in Year 5 of Primary Education.