Its survey of leading employers found that, while 54% of students are women, they make up just 47% of graduate scheme applicants.
But they took 49% of the posts, the responses by 170 employers showed.
"Many women don't apply for the top schemes when they should," said AGR chief executive Stephen Isherwood.
Improving the gender diversity of graduate programmes is largely a challenge of attracting women in the first place, says the report.
Once they apply women are more likely to be hired, according to the survey sent to AGR members in April this year.
Even in male-dominated areas such as IT and engineering, women are proportionally more likely to succeed once they decide to apply, the survey found.
For example, women make up only 17% of IT students and 15% of engineering students, but succeed in getting 27% and 25% respectively of the places on graduate schemes in these fields, the report suggests.
This means that while men make up 83% and 85% of the student population in these fields, they find it relatively tougher to get work - taking 73% and 75% of the jobs.
But in the field of law the reverse is true - 63% of students are female but only 58% of the graduate scheme posts go to women.
Graduate employers are making efforts to boost the numbers of women they hire, the research found.
Three quarters of the firms which responded to the survey had a diversity strategy in place, and the majority said redressing workplace gender imbalance was the highest priority.
Construction and engineering firms were particularly successful, increasing the share of women hires by 3% and 4% respectively in a year, says the report.
Mr Isherwood says considerable barriers to gender equality remain.
"Graduate employers want to hire women, there are lots of opportunities out there and these candidates are more likely to succeed, so we need to address why they're not applying.  Industry-wide collaboration to tackle student perceptions will be a key step forward.
"We know women are hugely successful in the selection process. We just need them to realise it. We need to boost confidence and encourage more female graduates to reach their potential."
Female students are less likely to aim for top graduate jobs but more likely to land them if they apply, says the Association of Graduate Recruiters.