Specific personality traits may predispose individuals to various forms of addictive behaviors. This study aimed to investigate the association between personality traits of university students and Internet addiction (IA). A sample of 1051 university students was recruited from the largest university in Eastern Croatia. A structured anonymous questionnaire that included questions regarding students’ sociodemographic information and Internet usage patterns, the Young Internet Addiction Test and Big Five Inventory served as a research tool. The study revealed that 1.0% of the studied sample expressed severe IA while 24.6% of study participants expressed some signs of addiction. The IA was detected in 576 (80.0%) students who used the Internet mainly for social networking, in 30 (78.9%) students who mainly used it for online gaming, and in 153 (52.2%) students who mainly used it for university assignments (p < 0.001). Higher neuroticism, higher extraversion, and higher openness to new experiences were connected with IA in general (p < 0.001). Higher neuroticism, higher extraversion, and higher openness to new experiences were significantly associated with addictive behavior during social networking (p < 0.001). Higher extraversion and higher openness to new experiences were significantly associated with addictive behavior during Internet usage for university assignments (p = 0.025), while there were no significant associations between specific personality traits and addictive behavior during online gaming (p = 0.059). Personality traits must be taken into account while developing programs and implementing interventions for preventing IA in the university student population.