Background: The smartphone ownership rate has been growing steeply worldwide, and there are various adverse effects of smartphone overuse. Previous studies suggest that adolescents are vulnerable to addiction because they lack the ability to control impulsive behavior. However, only a few studies have investigated psychological factors related to smartphone addiction predisposition (SAP) among adolescents. This study compared the prevalence of SAP in adolescents and adults and investigated associations between impulsivity and SAP. Methods: A total of 7003 participants answered the entire set of questionnaires. Participants completed self-report Korean questionnaires regarding demographic characteristics, level of SAP, and trait impulsivity. They were divided into three groups based on age: an adolescent group (14–18 years old), an early adulthood group (19–25 years old), and an adulthood group (over 26 years old). SAP was assessed with the Smartphone Addiction Proneness Scale (SAPS), and impulsivity was assessed with Dickman’s Impulsivity Inventory (DII). Results: The level of SAP was significantly different between age groups, with the adolescent group having the highest percentage of SAP. Dysfunctional DII score was highest in the adolescent group, and there was a significant difference between the adolescent group and the other two age groups. Moreover, the higher the level of SAP, the greater the dysfunctional impulsivity score. Conclusions: Result suggests that adolescents are vulnerable to SAP, which is similar to substance addiction and other types of behavioral addiction. In addition, impulsivity may be one of the factors contributing to this vulnerability, as it does to other addictions.