This study aims to explore how sleep quality act as a mediator between smartphone addiction and mental health problems among Vietnamese undergraduate students. In this study, self-report questionnaires, including the Smartphone Addiction Scale, Short Version (SAS-SV), the Depression, Anxiety, and Stress Scale, 21 (DASS-21), and the Pittsburgh Sleep Quality Scale (PSQI), were filled out by 905 students who had an average age of 19.83 years (SD = 1.30). 561 students, accounting for 62% of all participants do not suffer from smartphone addiction, while 344 students, representing 38.0% of all participants suffer from smartphone addiction. Female students exhibited a higher level of smartphone addiction compared to male students (p < 0.05). This study found a positive correlation between smartphone addiction and stress, anxiety, depression, and sleep quality. The relationship between smartphone addiction and mental health problems (stress, anxiety, and depression) was shown to be mediated by sleep quality. Several research and practice suggestions are provided.