Borg also wants to raise taxes on alcohol, tobacco and vehicles, as already mentioned earlier this week.
A bottle of wine or beer will be five percent more expensive, while taxes on cigarettes will be raised by three percent, and on snus by one percent.
Government agencies can also expect budget cuts, news agency TT reports.
The conservative Moderate finance minister says he expects the target of a budget surplus of 1 percent of GDP to be reached by 2018.
The proposals will form part of the Spring Budget, and would give the ruling centre-right coalition a margin for election promises ahead of this Autumn's General Election, TT reports.
The Social Democrat's economic spokesperson, Magdalena Andersson, says she is not in favour of cutting student grants.
"I think that is very strange logic, to make students borrow more because Anders Borg has wasted money. What does this government have against students and higher education" she told Swedish Radio News. Two other opposition parties, the Left Party and the Greens, also say they oppose the plans to cut student grants.
Green Party spokesperson Åsa Romson is critical. She told Swedish Radio News: "Borg's proposal makes a mockery given that the students are the group in society who have the least monthly incomes, worst opportunities in the housing market and are each day toiling to build the knowledge which is Sweden's future," says Åsa Romson.