Sir Steve Webb, director of policy at Royal London, wants the government to encourage more people to claim them.
Parents who give up work are given NI credits while their children are under 12, to help them get a state pension.
If they return to work, relatives can claim the credits instead.
To qualify for the so-called grandparents' credit, such relatives need to be of working age, while caring for the child in question.
In the year to the end of September 2016, only about 1,300 people claimed the credits, according to a response to a Freedom of Information request.
However, Sir Steve said that as many as 100,000 relatives could get them, if only they were made aware.
"The scheme is not much use if hardly anyone takes it up," he said.
"The government needs to act quickly to alert mothers to the fact that they can sign over the National Insurance credits that they do not need."
Any close relative can apply for the National Insurance credits, but it's most likely to be a grandparent, as long as they're under pension age.
Each year of caring for a child under 12, qualifies them for an extra £231 of annual pension.
Which is valuable if they don't have a full National insurance record and aren't earning enough to pay National Insurance anyway.
If families think they've missed out, they can make backdated claims for all the years back to 2011.
A grandparent or other relative who takes part in the scheme for a full year is able to claim an extra 1/35th of the state pension.
That is worth £231 a year, or about £4,600 over a 20-year retirement.
In response, the government said that as many as 5,000 people in total had benefited from the scheme - officially known as Specified Adult Childcare credits - since it started in 2011.
"These credits are available to people in a small number of specific circumstances," said a spokesperson for the Department for Work and Pensions (DWP).
"As with all credits, details of the Specified Adult Childcare credits are well publicised on GOV.UK and are promoted through a number of consumer websites."
Those who have missed out on the scheme can make back-dated claims.
The application form can be found on the government's website.
Tens of thousands of grandparents are missing out on National Insurance (NI) credits which could be worth more than £230 a year when they retire, a former pensions minister has said.