Poor mental health is common among university students every where, including in Bangladesh. Since information about mental health well-being (MHWB) of private university students are still scarce, this study aims to estimate the prevalence of poor mental health and associated determinants, using cross-sectional data (N=670) collected from undergraduate students of East West University. The WHO Well-Being Index, composed of five Likert Scale questions with possible answers from 0 (not at all) to 5 (all the time), was used to measure the state of MHWB using a cut-off 13 for the total score. The overall prevalence of poor mental health was 34.6%, and was significantly higher among female (38.9%) than among male (30.5%) students. Its prevalence was also significantly higher among students who had no close friends for sharing problems, and among students with low level of satisfaction about their current residences in Dhaka, academic performance at EWU, and relationship with faculty members. Since a large proportion of students suffer from poor MHWB, EWU administration should consider this as a serious issue and apply feasible prevention strategies in a comprehensive manner.