Retired bricklayer David Arloff and two friends sent the party cheques for £3 to become registered supporters.
But the cheques were returned with a letter explaining they could only pay online by credit or debit card.
Mr Arloff said the men "haven't got computers and we are not au fait with the internet".
The 72-year-old, from Stevenage, in Hertfordshire, said: "We are being denied the right to partake in this vote because we are not young and up and coming. It is ageism.
"There are people bragging that they are Conservatives and they are getting two or three votes, but genuine left-wing people like us are being denied the the opportunity.
"I am not a member of the London Federation of Anarchists or the Socialist Workers Party.
"I am just a former Labour Party member who wants to have a say."
He added: "There must be hundreds of people like us. I bet if I sent a cheque for a £100 as a donation, they wouldn't send it back."
The Labour Party does accept cheques from people who want to be full members, which costs £46.50 a year.
But a party spokeswoman said they did not accept cheques from people wanting to become registered supporters, because it was a new process.
She added:  "We want the widest number of supporters to have their say in Labour's leadership contest.
"To apply for a ballot paper through the new registered supporters scheme there were a number of ways supporters could have donated their £3 including, using a debit or credit card to pay over the telephone, online or by completing and returning a paper form or via text message.
"Out of the 120,000 people who applied to be a register supporter, less than 50 attempted to do so via cheque."
Mr Arloff and his friends, aged 78 and 80, had sent their cheques on 5 August, but the letter from the party had arrived after Friday, 15 August's registration deadline, he told BBC News, so even if they had wanted to pay over the telephone they would not have been able to.
Mr Arloff said he had left the Labour Party during the Blair years and had voted Conservative at this year's general election to send the party a message.
He been planning to vote for the veteran left-winger Jeremy Corbyn in the leadership contest, he added.
A pensioner has accused Labour of "ageism" after his application to vote in the party's leadership election was rejected because he had paid by cheque.