The base hosts four submarines armed with nuclear-capable Trident missiles.
According to the BBC, the campaigners gathered at Faslane at 07:00 GMT, attempting to stop workers from entering. The protest was organized by the Scrap Trident Coalition, and is set to last until 15:00.
As many as 40 police officers are present at the site, as demonstrators chain themselves to the gate of the base.
The renewal of the Trident program is a hotly-debated topic in the run-up to United Kingdom general elections next month.
According to UK Defense Secretary Michael Fallon, the Conservative party, if it wins the elections, intends to renew the Trident program by building four submarines.
According to local media, the Labour party, Conservative's biggest opponents, may join forces with the Scottish National Party, which is adamant about scrapping the Trident, in a bid to win more seats at the parliament. Labour's Shadow Defense Secretary Douglas Alexander said that his party was committed to the renewal of some form of minimal deterrent.
The UK general election is scheduled for May 7, 2015.