Screen media use is part of most children's everyday lives, but organisations have advised that use should be limited. The aims of this study were to describe 6-11-year-old Danish children's screen device ownership and screen media use (weekdays and weekends), including the role of parental education, family structure and household screen media rules. We conducted a cross-sectional study including 5274 Danish children aged 6-11-years sampled from ten Danish municipalities from May 2019 to November 2020. Characteristics of the sample and source population were obtained from the Danish Health Data Authority. Parent's completed the SCREENS questionnaire, which was developed to assess children's screen media habits. We used inverse probability weighted logistic and linear regression models. Smartphone and laptop ownership was higher with increasing age, and use of screen media varied across day type, age and gender. The proportion of children using screen media more than 4 h/day was 13% (95% CI 12%;14%) for weekdays and 28% (95% CI 27%;29%) for weekend days. Children of parents with medium-length or long educations had statistically significant lower odds of using screen media more than 4 h/day. We found a statistically significant graded relationship between household screen media rules and children's screen media use; the less parents reported presence of rules, the more time their children spent on screen media engagements. Our results suggest that parental educational level and family structure are related to unfavourable screen media habits, and household screen media rules may play an important role for parents to limit children's screen use.