More than a third of the poorest three-year-old boys displayed behaviour problems, compared with one in six of those living in richer households.
The study analysed the responses of parents to a questionnaire to compare the behaviour of children aged three to seven, rating their child's behaviour in terms of hyperactivity and inattention, conduct problems, emotional symptoms, and peer problems.
The findings, from researchers at Bristol University, show that the proportion of three-year-old boys from the poorest fifth of homes showing clinical level symptoms of behaviour problems was double that of three-year-olds from the higher four fifths of homes, in terms of income.
By the age of seven, a fifth of the poorest boys still suffered from behaviour problems, compared to one in 10 of those from richer homes.
• Rights way to better pupil behaviour
Among girls, the rates were lower, but nearly three in 10 of the poorest exhibited symptoms of behaviour problems, which dropped to a fifth at the age of seven.
The research suggests that the gap in behaviour has widened over the last 10 years.
Girls from low income families who were born in the early 1990s were twice as likely to display behavioural problems than their peers at age seven, while those born around the millennium were three-and-a-half times as likely to show such symptoms at age seven.
"Overall our results show that behaviour problem symptoms are much more common among children from disadvantaged backgrounds," the report said.
"More than anything, the research shows once again why it is so important to intervene pre-school to stem problems before they develop."