The study of more than 2600 families found that children whose fathers experienced depression when they were born are at heightened risk to have behaviour problems when they were between four and five.
The study leader, Richard Fletcher, said the research found maternal and paternal postnatal depression often occurred at the same time, creating a "worst case scenario" for their children.
The study found that the 1.3 per cent of fathers experienced symptoms of depression when their children were born, compared with 2.6 per cent of mothers.
International research had shown depressed fathers were less likely to read to or play with their children, and used more physical discipline on children as young as one.
"We don't want to blame these dads," the Age quoted Dr Fletcher as saying.
"But we do need to see plans put in place so we can pick them up," he added.
The study was recently published in The Medical Journal of Australia.