Social Networking Sites Addiction (SNSA) has become increasingly prevalent among university students, posing significant challenges to their mental health and academic performance. The psychological mechanisms and personality traits contributing to this addiction are not yet fully understood. This study explored the mediating effect of attachment avoidance (AA) between relatedness frustration (RF) and SNSA, as well as the moderating roles of Conscientiousness and Neuroticism from the Big Five personality traits. Data were collected from 489 university students (M = 18.81, SD = 0.92) using the Relatedness Frustration Scale, Ten-Item Personality Inventory in Chinese, Experiences in Close Relationships Scale (ECR) Short Form, and Social Networking Sites Addiction Scale. The findings were as follows: (1) RF significantly predicted SNSA; (2) RF significantly predicted AA, which in turn significantly predicted SNSA, indicating a partial mediation; and (3) Conscientiousness and Neuroticism moderated the effect of RF on SNSA, with higher levels of these traits amplifying the positive effect of RF on SNSA. The study concluded that individuals facing RF may avoid real-life attachments and seek connections online, increasing the risk of SNSA, especially for those with high levels of Conscientiousness and Neuroticism.