Purpose of the study: Due to increasing mobile Web penetration rates mobile Web surveys are gaining importance in survey research. However, coverage error is a major threat to mobile Web surveys. This study aims to estimate coverage error caused by citizens without mobile phones or by mobile phone owners without mobile Web access. Design/methodology/approach: Eurobarometer data from 2009 to 2013 across 27 European countries were used to calculate the relative coverage bias. Eurobarometer studies were administered face-to-face and, thus, provided relatively complete coverage. Questionnaires contained questions concerning mobile phone ownership and smartphone access. Thus, we were able to estimate  the no mobile phone bias and the no mobile Web bias as well as the joint coverage bias. Bias concerning various socio-demographic variables was assessed. Findings: Considering Eurobarometer data of 2013 about 90 percent of the European population reported mobile phone ownership. Mobile Web access increased from 32 percent in 2005 to 46 percent in 2013 which signifies a promising development for survey researchers. However, analyses revealed still remarkable coverage bias estimates for socio-demographic variables for the mobile Web population. Interestingly, coverage bias for the mobile Web population is mainly caused by people without mobile phone not predominantly by mobile phone owners without mobile Web access. The no mobile phone bias and the no mobile Web bias do not compensate to a great extent. Originality/value: Using mobile Web for surveys is an extension of the present use of online surveys and of the trend towards selfadministration and technology use in survey methodology (Couper, 2008). However, little is known about methodological problems of mobile Web surveys. Research shows that coverage bias is still considerably large but deteriorates over time. Thus, in the near future mobile Web surveys might become worth considering for survey data collection in the general population.  Research imitations/implications: Based on Eurobarometer data we cannot identify mobile Web users. We have to acknowledge that the mere coverage of the smartphone population does not imply that every smartphone owner is capable and willing to use mobile Web to take surveys. Practical implications: Given the fact that the relative coverage bias of the mobile Web population decreases for some sociodemographic variables, using this new technology as a survey mode in the general population comes into sight.