Cambridge University says about a third of its 12,000 undergraduates could benefit from an upgrading of its bursary scheme from 2006.
Vice-chancellor Alison Richard wants a wider range of undergraduates
Some 1,200 from the poorest families would get an extra £4,000 a year from the university.
The means-tested support would taper out at a family income of about £35,000, Cambridge said.
The scheme depends on the government's controversial plans for higher tuition fees in England going through.
Those plans are the most contentious in the raft of legislation announced in Wednesday's Queen's Speech.
As of Thursday lunchtime, 128 Labour backbenchers had their names on a rebel motion proposing that the government publish alternative models of funding higher education for debate.
The government hopes that the use of bursaries by universities will blunt people's concerns about debt putting off poorer students.
It is not yet clear whether its legislation - which might be published as early as next week - will involve any nationwide scheme.
The more elite universities have made clear their opposition to being forced to divert any extra income from higher fees into subsidising students at other institutions.
Its concern is to bridge the "poverty trap". This is the difference at the lowest end between the grant it is providing from next year, £1,000, plus the £1,125 fee remission, and the maximum "top-up" of £3,000 - a gap of £875.
If bursaries were offered to the poorest to cover that, ministers could say the poorest students would be no worse off under its plans even if they wanted to pursue the most expensive courses.
'Open to all'
Cambridge said that about one in 10 undergraduates would get bursary help equivalent to basic living costs - estimated at between £5,000 and £6,000 per year.
Eventually, the university said, it hoped to finance the £7.9m-a-year scheme "through a major fundraising drive".
The vice-chancellor, Professor Alison Richard, said: "I believe passionately that this university must be open to all outstanding students, regardless of background.
"Higher fees are only acceptable if we can be confident of this, and when I began my term as vice-chancellor in October, I wanted to be assured that we could create a comprehensive and navigable bursary scheme.
"I am confident that we have a proposal for such a scheme in hand."
It should "widen the pool of qualified students who will apply to Cambridge".
The plan has brought the university off the fence in favour of top-up fees.
Like other universities it argues that it needs the extra money.
Facts and figures
It says it is underfunded by £24m a year for undergraduate teaching. Overall it had a deficit last year of £4m.
"Only endowments and relatively low salaries have allowed Cambridge to maintain quality so far," it said.
Endowments of about £500m, built up over 800 years, generate annual income of about £49m, or 10% of its total.
But these are dwarfed by those of its US competitors and salaries are "steadily losing ground".
"More investment is needed in staff, students and facilities to sustain world-class performance."
The government's proposals to let it charge £3,000 fees would increase its income by about £20m.
The university's existing bursary scheme offers £1,000 a year to those in receipt of fee remission - government support which means the poorest do not pay the present flat-rate fee, £1,125 this year.
It says this is already the largest programme of UK undergraduate support, totalling £1.5m per year.