We investigated the factors associated with support for banning e-cigarette use in public places in the European Union (EU) and how this varies by socio-demographic determinants, use of tobacco, ever use of e-cigarettes and their perceived harm. Data are from the representative Special Eurobarometer for Tobacco survey performed in 2014 (n=27,801) in 28 EU member states. Analyses were conducted separately by tobacco use status (never, current, and former smokers) and e-cigarette experimentation status. 70.9% of never smokers, 63.1% of former smokers and 45.7% of current smokers in the EU supported a ban on the use of e-cigarettes in public places. In all groups, support for banning e-cigarettes in public places was lower among those who had experimented with e-cigarettes (adjusted odds ratios (aOR) 0.43 vs. 0.50 vs. 0.61, among never, current and former smokers respectively) and higher among those who perceived e-cigarettes as harmful (aORs 2.49 vs 2.35 vs. 2.40, among never, current and former smokers respectively). 40.5% of those who had experimented with e-cigarettes supported a ban on use in public places, although levels of support were lower among those who started using e-cigarettes in order to circumvent existing smoking bans (aOR 0.54, 95% Confidence Interval 0.45-0.64). Bans of e-cigarette use in public places in Europe have high levels of public support even among former and current tobacco smokers, although this does vary across population groups. As legislators consider approaches to e-cigarette use, public opinion is likely to become more important to the passing and enforcement of any legislation.