Purpose: This study assessed the relationship between electronic cigarette (e-cigarette) use and attempts to quit smoking cigarettes by adolescent smokers in Taiwan. Methods: Data were obtained from the cross-sectional Taiwan Global Youth Tobacco Survey conducted annually between 2014 and 2016, which included adolescents aged 12–18 years. The independent variable was e-cigarette use in the previous 30 days. The outcome variable was attempts to quit cigarette smoking during the previous 12 months. We controlled for the following variables: year of survey, gender, grade, monthly income/allowance, numbers of cigarettes per day, smoking status of parents and friends, use of other tobacco products, access to free tobacco products, assistance in quitting smoking, and exposure to anti-tobacco campaigns. Results: Among cigarettes smokers, the prevalence of current e-cigarette use (in the previous 30 days) increased from 9.82% (2014) to 27.46% (2016), whereas attempts to quit smoking cigarettes decreased slightly from 71.31% (2014) to 70.59% (2016). Current e-cigarette use (OR = 1.21) was positively associated with attempts to quit cigarette smoking. Smokers who observed anti-tobacco media messages (OR = 1.12), attended antismoking classes (OR = 1.17), were influenced by warnings on cigarette packages (OR = 3.32), or received help to quit (OR = 3.11) were more likely to have attempted to quit cigarettes. Conclusions: We identified factors correlated with attempts to quit smoking, and recommend that the government continue monitoring electronic cigarette use, combat smoking in the media, provide antismoking classes, and expand health warnings on cigarette packages.