Around 59 per cent of them are aged 40-plus, the survey from Hays Accountancy Personnel has found.
This compares to just 27 per cent aged 40-plus in local government finance departments, and 31 per cent of finance staff in the health service.
The study discovered that only 29 per cent of charities monitor the age profile of their finance departments, but respondents said that the age range had not changed significantly over recent years.
Andy Robling, director of the not-for-profit section at Hays Accountancy Personnel, said the comparatively older age of finance staff in the sector could be a problem for smaller and medium-sized charities.
"A lot of knowledge is tied up with older members of staff," he said.
"Some staff have been with organisations for over 20 years. It can be a positive thing. It adds stability and cohesion, provided you have succession planning in place.
It is a problem if you are not attracting young people into the organisation."
But Fiona Young, finance director with homelessness charity Crisis, said that the age profile in charity finance departments was beginning to fall, especially at director and manager level.
"In the past, a job in the finance team was seen as something you did as your last job before retirement, but this is changing now. Younger people are going into charity finance teams, as a career in the voluntary sector is seen as a better alternative than it used to be," she said.
Young's claim seems to be borne out by umbrella body the Charity Finance Directors' Group, which last September elected its youngest ever chairman, 32-year-old Paul Breckell of the Church Mission Society. He succeeded the more senior Geoff Miller of the British Red Cross.
But Young denied that the comparatively higher age of charity finance staff posed problems. "In itself it is not a problem - like all things in life you are often dealing with people's abilities and preconceptions. I think people can be set in their ways at any age."
One advantage the voluntary sector seems to possess over the public sector, according to the survey, is its working environment. Some 65 per cent of respondents from charities name a relaxed working culture as one of the main benefits of their job, compared to just 7 per cent of local government finance workers and 10 per cent in the health service.
Around 88 per cent of charity finance staff also cite the opportunity to contribute to public life as a benefit, and just under a third value flexitime.
Robling added: "Finance staff in charities don't want an oppressive regulatory culture, but to have more latitude. Charities have to sell that without giving the impression that they are slapdash."