The report suggests job prospects have improved for those leaving university this summer, with a rise in the number of graduate positions available.
But it warns that top employers are still receiving high numbers of applications for every role on offer, with some firms, such as consumer goods and media companies being sent more than 100 applications for each position.
Many well-known employers have already finished their graduate recruitment for this year, or closed off their application process early on.
Overall, there were an average of 46 applications for every graduate vacancy this year, compared to 51 last year, according to the study by High Fliers Research.
In 2008, before the recession, there were 35 graduates competing for each job.
Consumer good companies received 160 applications for each job this year, while media firms received 110.
The report also suggests tough competition among graduates hoping to work in banking and finance or the oil and energy fields, with these industries receiving 84 and 74 applications for each opening respectively.
The study, which looks at graduate vacancies and starting salaries among 100 leading employers, found that these firms have increased the number of vacancies on offer by 4.6% more than expected.
Half of the firms questioned said they had expanded their graduate recruitment this year, with 24 offering at least 20 extra jobs compared to last year.
Around a fifth of organisations have kept their graduate jobs at the same level, while a third have cut the number of vacancies they offer this year.
The report says that in nine of 13 industries there has been an increase in graduate job openings, including engineering and industrial areas, the public sector, consumer goods, media, law, investment banking, accountancy and professional services, oil and energy and the Armed Forces.
But there are fewer jobs available for those hoping to work in retail, banking and finance, IT and telecommunications and consulting.
In total, as of this month, there were 17,217 graduate vacancies for 2013 among the firms surveyed, the report suggests.
The typical starting salary for new graduates has remained static at £29,000 for the fourth year in a row.
Martin Birchall, managing director of High Fliers Research, said: "It's great news for the 'Class of 2013' leaving university this summer that graduate recruitment at Britain's top employers is now at its highest level for five years and that many of the country's best-known organisations are set to expand their graduate vacancies even further in 2014.
"But our latest research shows that competition for individual graduate jobs remains fierce, with employers receiving an average of 46 applications per vacancy this year."