Substance abuse and addiction are among the most important biological, psychological and social issues that affect all societies. This study was designed to investigate the simple and multiple relationships between family function and personality characteristics (neuroticism, extraversion, openness, conscientiousness and agreeableness) with addiction potential among the male high school first graders in Ramshir. The sample consisted of 218 students selected through simple random sampling. For data collection the Family Assessment Device (FAD), the Neo Five Factor Inventory (Neo-FFI) and the Iranian Addiction Potential (IDP) were used. Data analysis showed that there was a negative relationship between family function and addiction potential. Also, there was a positive corrolation between neuroticism and addiction potential. The extraversion, openness, conscientiousness and agreeableness factors had a significantly positive relationship with addiction potential. The results of multiple regression showed that family function, neruticism and agreeableness were significant predictors of addiction potential. It is concluded that addiction potential is influenced by family function and personality characteristics.