In recent years, mobile devices are increasingly considered to access the Word Wide Web. Several survey research organizations are about to use this technology as a means of conducting self-administered surveys. Among other advantages it allows survey researchers to overcome the lack of random selection procedures in online surveys since it provides the opportunity to use RDD-like probability sampling of cell phone numbers. However, low penetration rates of smart phones raise concerns that the coverage bias of a mobile Web survey might in fact harm survey estimates considerably. In this paper, we report results of a simulation study on the coverage bias of the mobile Web population across European countries. Based on a subset of the Eurobarometer data we estimate the relative coverage bias of the smart phone population in contrast to the general population. Even though we observed an incline of the mobile Web penetration rates over the course of the past years, coverage biases were still considerably large for socio-demographic variables. Nevertheless, in a few European countries mobile Web coverage biases are already smaller than the coverage biases of the population with traditional landline Internet access.