"Our forces are in full control of Tagreft barracks and military engineers are inspecting the zone to clear anti-personnel mines," the forces of the Government of National Unity (GNA) said on Facebook.
It said the fighting 20 kilometres (12 miles) outside Sirte left six dead and 15 wounded.
A second barracks, named Al-Jalet, was also seized as well as a bridge and an intersection that leads to the western entrance to the city of Sirte, it said, in operations backed by seven strikes by the Libyan air force.
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The GNA forces said one of the air raids destroyed a booby-trapped truck before it reached their lines.
Anti-personnel mines and booby-trapped vehicles left behind by retreating IS fighters were failing to slow the GNA forces, they said.
The unity government's forces and those of a rival authority in the east are currently engaged in a race to be the first to drive IS out of Sirte, the hometown on the Mediterranean of Libya's ousted dictator Moamer Kadhafi.
The international community believes this could jeopardise efforts to defeat IS, whose threat has grown since it established a foothold in Libya at the end of 2014.
The UN's special envoy on Libya, Martin Kobler, has called on the rival administrations set up since the fall of Kadhafi in Libya's 2011 revolution to "unite their efforts" into a single army.