The study led by doctoral researcher Dr Pene Schmidt also found that children, who are not in the average weight range, are also more likely to over or underestimate their body size.
The researchers analysed the data of more than 2100 Victorian children aged 4-12 and their parents.
They found that almost 43 per cent parents of underweight children tend to overlook the problem considering it the normal weight.
On the other hand, nearly 49 per cent parents of overweight children incorrectly believed their child was average weight.
Moreover, parents were more likely to report that their sons were underweight and that their girls were overweight.
"Parents are unlikely to take the necessary preventative actions if the perception of their child's weight - whether underweight or overweight - is incorrect,'' said Schmidt.
It also showed that only 4 out of 10 underweight girls and half of underweight boys correctly assessed their weight.
"This study also suggests a strong social bias among both parents and children towards thinness,
"While public health campaigns are directed towards the prevention of obesity, it's also important that the messages are getting through to the right groups."
"In particular we need to make sure that the focus on reducing the number of overweight children does not have the adverse impact of increasing the number of underweight children," she added. (ANI)