Every Master and PhD student at the Open University of Tanzania (OUT) has to make a research project as one of the requirements for completing their degree programmes. However, most students at the OUT face challenges in their research writing process due to lack of the research writing skills. This paper discusses the research writing skills and other challenges which the Master and PhD students face at the OUT. The challenges were learned from the researcher’s personal experiences of five years in supervising and training students on research methodology course for Master and PhD students at the OUT. Foremost, this paper presents the sections of the research proposal and research report which are mostly problematic to students and the author provides the suggestions on improvements. These sections include background information, the problem statement, research objectives, theoretical and empirical literature review, the research gap, research design, approach, strategy and philosophy, variables and measurements, data analysis, results and interpretation and conclusion and recommendations. Secondly, the paper also discusses other challenges which hinder students’ theses and dissertations timely completion at the OUT which include insufficient research orientation, lack of reading culture lack of facilitation methods’ integration for research course trainers, lack of awareness on students-supervisors responsibilities, lack of research completion strategy, low level of English language proficiency and lack of funds and health problems. Finally, the paper presents conclusions and recommendations for improvements.