Plagiarism is an act that is capable of tarnishing the image of universities and postgraduate students need to avoid it. However, interactions with postgraduate students revealed that some of them did not consider some acts that constitute plagiarism as such due to ignorance. Besides, literature search showed that due attention appears not to have been paid to the issue of plagiarism policy in most universities in Nigeria. Thus, this study empirically examined the awareness of plagiarism acts and policy by postgraduate students in University of Ibadan, Nigeria. Descriptive survey research method was used and the study population comprised 26,503 postgraduate students of the University of Ibadan, Nigeria. The multistage random sampling technique was used to select a sample size of 226 and the questionnaire was used to collect data. Findings showed that most of the respondents 171 (86.4%) were aware of what plagiarism is and majority were also highly aware of the different acts that constitute plagiarism. Results also revealed that a significant proportion of the postgraduate students 110 (55.6%) had low level of awareness of existence of a plagiarism policy in their university. Majority of the respondents had high level of research competence in avoiding plagiarism. It was recommended that the postgraduate school and faculties hold workshops every academic session to strengthen the research competence of postgraduate students and train them on how to use other people’s intellectual works without plagiarising. The management of the university should also ensure that plagiarism policy is formulated and implemented.