An argument in academic writing is an essential element; it is used to convince readers that the writer's opinion or claim can be acceptable. However, this may be problematic for university students or new writers especially when writing in a language other than their first language such as Indonesians who take an international English writing test. The aim of this study is to identify and describe the rhetorical features of successful academic IELTS essays. Sixty academic essays were taken from six different common topics with band scores 8-9 (high quality essays) and were analyzed on elements of argument following Toulmin (1979). The results show that: a) the common sections found in the essays are lead in, thesis statement and deduction; b) the common elements of argument in the essays are claim, data and warrant; and c) the common types of argument structures of the essays are simple argument structure and strong argument structure. This implies that the essay sections, argument elements and argument structure can be used to describe the quality features of IELTS essay organization. It is suggested that in order to be able to write good quality essays in English, test takers must have a good command of essay sections, argument elements and argument structure type of good quality essays.