Students from Wolverhampton who go to Codsall community high in neighbouring Staffordshire get up to pound;30 a week to stay on in the sixth-form. Their classmates who live in the county do not benefit from the scheme.
Nigel Caine, a South Staffordshire Conservative councillor and a governor at the school, said the education maintenance allowance scheme, piloted by Wolverhampton city council, was causing bad feeling.
He said that up to 20 per cent of the sixth form's 360 students were in receipt of the payment.
Mr Caine said: "The kids from Wolverhampton are from socially depressed areas, coming over the border and getting pound;30 a week to come to Codsall. They have got loads of money and are going down to the tuck shop and throwing it around."
He added: "If Wolverhampton wants to encourage their pupils to stay on in the sixth form, they should be staying on in schools in their area. If they come here they should forgo the money Wolverhampton pays them."
A spokeswoman for Staffordshire county council confirmed that pupils from Wolverhampton attending Codsall were getting grants as part of the government pilot scheme focusing on urban areas.
No one from the school was available for comment.