"Over the next 100 days we must have allocations of around $100 million provided so that the minister (of education in Lebanon) can increase the enrolment in his schools," Brown told a news conference in Beirut.
Lebanon has an official population of four million, but it is estimated to host 1.2 million refugees who fled the conflict in neighbouring Syria over the past four years.
The country's education minister, Elias Abu Saab, says that little more than 100,000 of the 400,000 school-age refugees from Syria actually enrolled as students last year in Lebanon.
"We have climbed one mountain, and made it possible for 100,000 refugee children to get to school, but we must now climb another mountain, and we must do it very quickly," said Brown.
"Of course we want them to be able to return to their home country as early as possible and to build education services in Syria, but as long as (these children) are here it's vital that we could extend to more children the opportunity of education."
Abu Saab said Lebanon has already received $100 million from the international community, allowing it to put 100,000 Syrians through school and pay teachers who have been doing extra shifts, including at night, to handle the influx.