More than four in 10 parents with underweight and overweight children think they are in the average range.
Melbourne University researchers also found that different methods of assessing children's weight - such body mass index (BMI) or waist circumference (WC) - result in their being categorised as overweight or underweight.
More children were classified as overweight according to BMI than according to waist circumference. The study by Pene Schmidt also found that children who are not in the average weight range are more likely to over or underestimate their body size.
It also found a small number of parents believe their underweight children are overweight or that their overweight children are underweight.
Schmidt, who completed her study in the University of Melbourne's School of Behavioural Science, analysed data from a survey of more than 2,100 Victorian children aged between four and 12 and their parents.
Schmidt made a pitch for overhauling ways in which children's weight is classified and provide better information to parents about appropriate weight at both ends of the spectrum, according to a Melbourne University release.
"Parents are unlikely to take the necessary preventive actions if the perception of their child's weight - whether underweight or overweight - is incorrect," she said.
While previous research has examined parental perceptions of overweight children, Schmidt's study is believed to be the first to also examine attitudes toward underweight children using both BMI and WC.