David McCullough, chief executive of WRVS, formerly the Women's Royal Voluntary Service, said he could not understand why councils and health boards commissioned private care providers.
"Why commission all our services from people who have to pay people to do it for them?" he asked. "We do amazing things and we do them from choice."
Mr McCullough made the comments at a conference on the role of food and nutrition in tackling loneliness, held by WRVS at the Scottish Parliament.
He said that while rising numbers of people over the age of 85 mean that services are needed more than ever, numbers of older people in early retirement are rising faster, and this is a key group willing to volunteer.
"The people available to volunteer may be growing faster than those in most need," Mr McCullough said.
He added: "There are councils still measuring care in minutes. What we are saying is, why don't you use organisations that don't have to count the minutes?
"When we turn up with our volunteers, we don't have that. There is the chance to talk, have a cup of tea.
"We match people with volunteers, and when the carer turns up it isn't a new person, different from the last week and the week before."
Volunteers include retired social workers, doctors and people from all walks of life who had skills that should be used, Mr McCullough added.
He challenged the suggestion that volunteers are less reliable than paid staff.
"There is a suggestion that if you pay people, they are always there, but volunteers might not be: that's rubbish.
"When people are doing this stuff from choice they turn up because they want to do it and it is seen as an obligation," he said.
"People who commission social care start from the point that we must have paid people delivering this service. But it's not true."
Mr McCullough also argued that there is a danger in providing care but not purpose for elderly people, and suggested health care should be designed to avoid this.
"We could end up with a nation of people with fantastic hips but nothing to live for," he warned.
The conference was preceded by a call for action to address the "extreme loneliness" suffered by thousands of elderly people in Scotland.
A survey for the WRVS found 26% of those aged 75 who lived alone described themselves as lonely and 5% of older people living on their own said they sometimes went for days without speaking to another person.
The event was opened by Scottish Health Secretary Alex Neil.
He said nutrition was critical for elderly people and added: "One in five people admitted to our hospitals are undernourished or malnourished and that is something we all should be ashamed of."
Praising charities such as the Dumfries-based Food Train, he added: "It is important that people living alone, or living isolated lives, get the nourishment they need, or they will not be able to face up to the challenges of modern living."
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