About 12 students stormed the offices of LSE director, Sir Howard Davies Students and 150 held a rally outside.
The LSE says it is reconsidering links with Libya "as a matter of urgency".
But the students demanded the university paid back the £300,000 it had accepted of a £1.5m grant from a charity wing of the regime.
The grant was pledged in 2009 by the Gaddafi International Charity and Development Foundation.
The funds have so far been used to develop a research programme on North Africa, focused on politics, economics and society.
The student demonstrators called on the LSE management to "repay" the £300,000 already spent by creating a scholarship fund for underprivileged Libyan students.
The students also urged the university to revoke the LSE alumni status of Libyan leader Col Gaddafi's second son Saif al-Islam, who studied at the university from 2003 to 2008, gaining both a Master of Science degree and a doctorate.
They called for a public commitment that no grants from officials "of such oppressive regimes" would be accepted in the future, as well as a public statement  denouncing the recent "gross violations of human rights" by the Gaddafi regime.
One of the protesters, Ashok Kumar, who is also education officer for the LSE students' union, said: "I think it's reprehensible that the university continues to benefit from money that was stolen from the Libyan people and it's only right to return it to the people who are now being murdered in the streets fighting for their freedom."
The money should be returned either as scholarships to underprivileged students, or "to the families of those who have been murdered and who continue to be murdered", he said.
In a statement, the university said the LSE Director "noted the message" from the  students.
"He shares the students' revulsion at the recent violence and gross violations of human rights in Libya, and much regrets the association of the School's name with Saif Gaddafi and the actions of the Libyan regime.
"The School's statement of 21 February made clear that School engagement with the present Libyan authorities, covering a number of programmes, has already finished or has been stopped following the events of the weekend of 19-20 February."
The university said no more of the £1.5m donation from the Gaddafi International Charity and Development Foundation would be accepted.
It said about half of the £300,000 already accepted had been spent and its  council would now consider what to do with the remaining funds, taking into account the views of LSE students.
The LSE's review of its links with Libya follows a speech made by Saif al-Islam Gaddafi on Sunday, in which he said the regime in Libya would stand firm.
He warned of civil war, talked of "rivers of blood" and rejected foreign intervention.
Saif al-Islam Gaddafi wrote his doctoral dissertation on the role of civil society in the democratisation of global governance institutions.
Students at the London School of Economics have staged a protest against the university's association with the regime in Libya.