In this paper we present the results of a cross-sectional study of the entire adolescent student population aged 12–18 of the island of Kos and their parents, on Internet safety-related practices and attitudes towards the Internet. Total sample was 2017 students and 1214 parent responders. Research material included extended demographics and an Internet security questionnaire, the Internet Attitudes Scale (IAS) for parents and the Adolescent Computer Addiction Test (ACAT) for children and both parents. Both parents thus provided their views on their children's computer use and an estimate for their degree of computer addiction which was tested against their child's self-report. Results indicated that fathers and mothers who had negative views of the Internet, tended to encourage less their children to engage in online activities and worried more for the possibility that their child is addicted to computer use; their worries weren't correlated with their children's results. Parental views on the Internet had no effect on the level of security precautions they employed at home. Those parents who reported a low level of security knowledge and were unsure as to what their children were doing online, tended to consider their children more likely to be addicted to computer use; those views were confirmed by their children' self-reported results.