The council is to work with JobCentrePlus and training organisations in Edinburgh's social inclusion partnership areas to target the unemployed.
Departments hardest hit are education, with 222 vacancies, and city development, with 110. Recruitment of low-paid staff such as clerical workers, road sweepers and toilet attendants, has been especially tough.
Full-page adverts, psychometric testing and a massive home-help recruitment drive at Murrayfield stadium have all been tried.
Frank Russell (Lab), Edinburgh's executive member for corporate resources, said: 'Part of the problem is that the Edinburgh economy is booming. There are plenty of jobs and it's difficult to recruit. But there are still pockets of unemployment, so hopefully this scheme will solve both problems.'
The report acknowledges 'difficult to fill' positions, many temporary or part-time, are not attractive to those on benefits.
'We're tied to national payscales, but can look at other conditions - for example flexible working - to make jobs attractive to women and other carers,' said Mr Russell.
'As far as I am aware, it's the first scheme of its kind.'