Severe abuse of social media has currently become a threat to social sustainability. Although “responsible use of social media” has recently attracted academics’ attention, few studies have investigated the psychosocial antecedents of individuals’ intention to use social media responsibly (IUSR). Therefore, the current study tested whether attitudes, self-control, and prosocial norms (ASP) can positively and significantly predict social media users’ IUSR. To this end, the theoretical interrelationships among ASP were explored, and an initial pool of items was developed by reviewing the relevant literature. Then, the items were selected based on a panel of experts’ content validity test. An online questionnaire was used to survey university student social media users (n = 226) in Bangladesh. PLSc-SEM and CB-SEM bootstrapping, followed by an artificial neural network (ANN) analysis, were completed to evaluate the measurement and structural models. Current results show that the three elements of ASP strongly correlate with and significantly influence each other, but attitude and prosocial norms partially mediate the relationships between the antecedents and intention. The predictors in the proposed model substantially predict and explain IUSR, which is supported by results of relevant past studies in different disciplines. Thus, the model expresses its applicability as a modified theory of planned behavior (TPB) in researching individuals’ social media behavior. The study has implications for relevant stakeholders to take crucial measures to promote more responsible use of social media. Limitations and avenues for future study are also presented.