The former Prime Minister, the UN special envoy for global education, is backing a plan to operate Lebanese schools on a "split shift" system.
There are now an estimated 440,000 Syrian refugee children in Lebanon, with thousands more arriving every week.
The sheer number of school-age refugees has seen the situation likened to that of Glasgow schools being forced to teach children from all of Scotland's other major cities put together.
Mr Brown warned of the dangers of a "lost generation" of young Syrians.
He said: "By fighting for the fundamental right to education for the children of Syria, we can establish the principle that even in the most hopeless of situations learning can continue."
The proposals would allow Syrian refugee children to receive an education without the need to build hundreds of extra schools.
Instead, Lebanese schools would open to Syrian children outside normal hours.
Syrian teachers forced to flee the conflict in their country would be among those recruited to cover the extra shifts.
The Kirkcaldy and Cowdenbeath MP and others involved in the proposals are confident they cam enrol Syrian children in school within weeks, if there is enough funding.
Mr Brown called on the public to donate money and press international agencies to back the plan.