Foods rich in sugar have been suggested to contribute to the increasing prevalence of obesity in children. The aim of this report is to investigate the dietary pattern in 1-year-old children who frequently receive foods rich in sugar but low in nutrients and to study associated demographic and parental factors. During 1977–9, 21 700 infants were invited to participate in this prospective, population-based, longitudinal cohort study. Screening questionnaires were completed for 16 070 infants after delivery. Follow-up questionnaires from 10 762 children at 1 year of age are included in the analysis. It was found that 24 % of the children received sweets/pastries more often than one or two times per week. They had a higher intake of French fries, potato crisps and cream as well as a lower intake of fruit and vegetables. A frequent intake of sugar-rich, low-nutrient foods was significantly associated with several maternal factors (high intake of sweets/pastries during pregnancy, young age, mother living alone) as well as presence of older siblings. Maternal smoking during pregnancy and maternal overweight were of borderline significance. Parental education level was inversely associated with the frequency of intake of sweets/pastries in the child. Children who frequently receive sweets/pastries also have an otherwise unfavourable dietary pattern. Several parental and demographic factors were associated with this feeding pattern, especially high intake of sweets/pastries during pregnancy. Screening of pregnant women for risk predictors like consumption of sweets/pastries, young age and smoking could be possible ways of identifying children at future risk for low dietary quality.