Aswad was born in 1975 when the band mates met each other in Ladbroke Grove, West London.

The original band was made up of guitarist/vocalist Brinsley "Chaka B" Forde, drummer/vocalist Angus "Drummie Zeb" Gaye, lead guitarist/vocalist Donald "Dee" Griffiths, bassist George "Ras" Oban, and keyboardist Courtney "Khaki" Hemmings. They started as a backing band for Burning Spear's 1977 Live album recorded at the Rainbow Theatre in London.

They began producing music in the roots reggae vein with Forde acting as the band's principal songwriter. But soon after the release of their self-titled debut album in 1976, the band saw a quick succession of changes. 

Hemmings left and was replaced by Tony "Gad" Robinson (the only time in the band's history where a departing member would be officially replaced by an incoming musician.

The band released their second studio album, Hulet, in 1978, before Oban departed the band in 1979.  Robinson took over as bassist and continued on the keys. The following year Griffiths departed, leaving Forde as the band's sole guitarist. During this early period in the band's history, they set themselves apart by writing songs that dealt with the issues of young people of the African diaspora growing up in the UK such as "Three Babylon" and "It's Not Our Wish", and the powerful jazz-influenced instrumental "Warrior Charge".

The trio of Forde, Gaye, and Robinson took Aswad in a new direction, gaining a wider audience with their 1981 album New Chapter. The Michael Reuben Campbell-produced A New Chapter of Dub LP soon followed, which was a dub of the entire New Chapter album.

In August 1982, Aswad played live at Meanwhile Gardens on the Sunday of the Notting Hill Carnival; the resulting live album Live and Direct with single "Love Fire" gaining wide recognition when it was used as the backing rhythm for Dennis Brown's "Promised Land".

They stormed the charts with classic covers like "Don't Turn Around" (a UK No. 1 hit in 1988), "Give a Little Love", and the reggae-flavoured rendition of "Best of My Love".

They contributed the single "Set Them Free" to the Greenpeace Rainbow Warriors album. And in the same year, they performed together with Cliff Richard the song "Share a Dream", recorded the previous year at Wembley Stadium as part of The Event (16 and 17 June 1989).

The band also holds the distinction of having played with each one of the ex-Wailers.

The band has toured extensively, playing across the World from London's Royal Albert Hall and Montego Bay's Reggae Sunsplash, to gigs in West Africa, Israel and Japan.

Aswad released their final studio album to date in 2009 entitled City Lock. They released the singles "What Is Love?" and "Do That Thing" in the same year.