In the studies of academic writing, graduate-level research writing practices across disciplines have gained increasing scholarly attention in recent years. However, most studies focus on English-as-a-second-language graduate students at the stage of thesis/dissertation writing in English speaking countries. Relatively less work has been conducted on new graduate students in non-Anglophone or English-as-a-foreign-language settings. The purpose of this study was to investigate the concerns and difficulties that first-year graduate students encountered while writing disciplinary research papers at a Taiwanese university. The findings show that research-related and linguistic-related issues are two major difficulties. While research-related issues, such as locating relevant literature and lack of helpful library support, were more of a concern for international graduate students, linguistic-related issues hindered the research writing process of both local Taiwanese and international students. In addition, a lack of disciplinary reading and writing skills posted another problem among these students. Pedagogical implications will also be addressed in light of facilitating first-year graduate students’ disciplinary writing practices.