The associations of Internet addiction (IA) and smartphone addiction (SA) with mental health problems have been widely studied. We investigated the effects of IA and SA on depression and anxiety while adjusting for sociodemographic variables. In this study, 4854 participants completed a cross-sectional web-based survey including socio-demographic items, the Korean Scale for Internet Addiction, the Smartphone Addiction Proneness Scale, and the subscales of the Symptom Checklist 90 Items-Revised. The participants were classified into IA, SA, and normal use (NU) groups. To reduce sampling bias, we applied the propensity score matching method based on genetics matching. The IA group showed an increased risk of depression (relative risk 1.207; p < 0.001) and anxiety (relative risk 1.264; p < 0.001) compared to NUs. The SA group also showed an increased risk of depression (relative risk 1.337; p < 0.001) and anxiety (relative risk 1.402; p < 0.001) compared to NCs. These findings show that both, IA and SA, exerted significant effects on depression and anxiety. Moreover, our findings showed that SA has a stronger relationship with depression and anxiety, stronger than IA, and emphasized the need for prevention and management policy of the excessive smartphone use.