The error occurred as the company was changing over to the new online operating system.
Mrs Yo Hearne, whose baby is cared for by a childminder, said two payments were taken from her e-voucher account in October.
She initially thought a payment on 9 October was her usual payment taken early, but when she checked her account on 2 November she discovered another payment had gone out on 23 October.
'It transpired two payments had gone out to my childminder,' said Mrs Hearne. 'We received no call whatsoever.'
Computershare said that the transition to the new system had been 'seamless' for the 'vast majority' of childcarers, employers and parents, but that 'a small number of people' were affected and that the company had contacted parents and childcarers immediately after the incident to apologise.
Mrs Hearne said that she spent 45 minutes on the phone to call centre staff trying to sort out the problem.
'At least if you have a complaint with your bank you know who to complain to,' she said. 'At least four times in the past I have had to complain about either missed payments or duplicated payments.'
She said that mistakes were not fair on childcarers who depended on vouchers for their income.
Childminder Linda Eames from Haringey, who looks after two children whose parents use Computershare, also received incorrect payments last month.
She said, 'Luckily I have a good relationship with the parents, but I shouldn't have to keep telling them I haven't been paid. It puts you in a bad position.'
In August she was paid twice for one child, but the same child's nursery did not receive their voucher payment.
'I had to take money out of my account and give it to the parent so she could pay her nursery,' said Ms Eames. 'You shouldn't have to go chasing your wages every month. I've never had an e-mail or a phone call when errors have been made.'
In a statement, Computershare said, 'We became aware that for a small number of people, the transition resulted in payments for childcare being taken from parents' accounts without notification. We immediately called the parents affected by this, apologised, and explained what had happened. We gave them an open choice of how they would like to resolve the situation and then called carers to apologise, let them know of the issue and offer them the same personal service.'
- See 'Analysis' about employer-supported childcare, page 10