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This research was conducted to see the challenging that faced by EFL students University students in writing Argumentative Essay. The method used is qualitative approach which involved content analysis. The researcher collect the data through interview and analyze the students’ argumentative essay using characteristics of critical thinking based on theory Cottrell (2005) and also use score rubric to see the level of the students’ critical thinking based on the elements of critical thinking that was adopted from Stapleton with combination with Jacob et al to categorized the students from elementary, pre intermediate, intermediate, post intermediate and the last one advance level in critical thinking. The participants of this research were 27 students of UNTIRTA (Universitas Sultan Agung Tirtayasa) Serang Banten who were majoring in English Education. The result show that only 9 students stated their standing point clearly, only 9 students stated their reasons clearly, 7 students stated their evidence properly to strengthen their argument, and only 6 students made opposing arguments clearly. Furthermore only 7 students made clear conclusion based on their evidence. The last one only 7 students consistent in writing from the first paragraph starting from thesis statement into conclusion. Most of students in this class (33% ) are in preintermediate level because most of them still difficulty in write supporting reasons to strengthen their idea.