In fact, four out of ten parents of children with overweight or obesity are even worried that their child will get too thin, researchers said.
The study included parents of more than 16,000 children, including 1,800 children from Sweden.
In the study, the parents were asked to estimate their child's weight status and health, and to describe their own worries about their child's becoming overweight or underweight.
The parents' perceptions were then compared with the children's actual measurements.
Around 40 per cent of parents of children with both overweight and obesity are worried that the child will become underweight.
Among parents of children who are already underweight, the proportion that are worried about it is 33 per cent.
One out of two parents of a child with overweight in Central and Northern Europe perceived their child's weight as normal. In Southern Europe, the same figure was 75 per cent.
"Our studies show that the parents' insight into obesity in their children indeed grows in pace with the child's age and higher BMI in the child, but also that a weight development at preschool age can go from overweight to obesity without necessary lifestyle changes being made," said Susann Regber, from the University of Gothenburg.
"Many parents simply do not see the increase in growth, and are dependent on objective information from, for instance, child welfare centres and school health care to act," she said.