Reverend Percival William Gibson, then Bishop of Jamaica, as a private co-educational secondary school of the Anglican Diocese, on a 25-acre site in suburban May Pen.

Construction of the first modern block of classrooms began in 1959 with fundraising by Leigh D. Phillips (later Foundation PTA President, 1962-1967) at the request of the Headmaster, and by the beginning of the Easter Term 1962, there were 236 pupils in attendance.

Glenmuir was modeled on the British public school and in the early years, half the teachers were English expatriates.

The second headmaster was Mr. Clement Radcliffe, a graduate of the University of the West Indies (UWI) who was educated at Glenmuir and who served as Head of the Inter-Secondary Schools Sports Association (ISSA).

House competitions began in 1960 with football and table tennis, gradually expanding over the years to a variety of sporting events, including field competitions, a cross-country race, and Sports Day, which centers around track and field events.

In recent years, the houses also compete annually in Eisteddfod, which features music, dance, song, and oratory performances.

They had made it into JCDC Nationals where they achieved 3 gold trophies with the performances "the Battle of Jericho", Witness, and Armageddon medley.

The lyrics emphasize the pursuit of knowledge, truth, and excellence, reflecting the school's motto.