Its monthly measure of conditions and trends in the UK job market revealed job opportunities in October 2012 grew by 4% month on month and 8% compared with the same period last year.
Reed claimed the index has now shown positive growth during each quarter of 2012, reinforcing the message of continued buoyancy in the jobs market.
Alex Perry, director of recruitment firm Leverage Partnership, told HR magazine: "There is still a large amount of caution being showed by employers.
"Everyone is still completely unaware of what will happen in 2013 and even though job figures are improving no one knows exactly what will happen next year."
Reed said one reason for the rise in jobs is that wages have remained flat compared with the same period last year and the figures also show that salaries are 3% lower than in the same period in 2009. Reed claimed this is further enabling employers to recruit.
James Reed, chairman of Reed, said: "The figures are based on real vacancies from employers across the UK and represent a true picture of what's happening in the job market right now.
"While others may debate what next quarter's GDP figures will bring, the position in the jobs market continues to be one of steady, sustained growth, as it has been for the year as a whole so far."
He added: "The figures point towards a buoyant pre-Christmas period for the jobs market with seasonal industries such as sales and customer service already recruiting roles in encouraging numbers."
The Reed job index tracks the number of new job opportunities and salaries on offer compared to the previous month. It is compiled by data drawn from online job vacancies.
