Scientists suggest they have found a reason why some shorter children perform less well at school.
Children's development is affected by a number of factors
A Children of the 90s study by the University of Bristol found low growth hormone levels were linked to low IQ.
The Pediatrics study suggests it would be possible to use diet to increase levels of the hormone.
But other experts said, even if growth hormone levels did play a role, it would be a tiny part of the "jigsaw" of factors which affect development.
It is already known that low birth weight babies develop more slowly, reaching development milestones later and having slightly lower IQs than normal weight babies.
Short stature, linked to poor post-natal growth and nutrition, is also known to be related to poorer performance in intellectual development tests and in educational achievement.
The Bristol team looked at what might happen in the body to explain these links, focusing on insulin growth factor (IGF-I) .
Circulating levels of insulin-like growth factors are influenced by a variety of factors, including diet, and control the effects of growth hormone on tissues.
IGFs play a key role in physical growth and organ development in childhood.
It has been suggested that they could also affect the development of the brain.
In the study, the researchers asked 547 children to complete an intelligence test at the age of eight.
Researchers also measured levels IGF-I in their blood.
They found that for every 100 nanograms per millilitre increase in IGF-I levels, verbal IQ increased by three points.
Professor David Gunnell, who led the research, said: "This study provides some preliminary evidence that IGF-I plays an important role in human brain development and may underlie the associations of birth weight and height with IQ."
He stressed further research was needed.
But he added: "As IGF-I levels are modifiable by diet and other environmental exposures, this may be one pathway through which the childhood environment may influence neurodevelopment. "
Professor Gunnell added: "Further support for this association comes from a recent study in which 74 low birth weight children were treated with growth hormone therapy and followed up for over two years.
"The therapy led not only to improved growth but also to improvement in IQ."
But Dr Harvey Markovitch, of the Royal College of Paediatrics and Child Health, said: "The researchers have found there is an associated between growth hormone levels and IQ.
"This could be a small piece of the large jigsaw of factors which determine child development."
But he added: "That doesn't mean there is a causal effect. It could be that both things are affected by a third factor."