"There were at least six attackers and several of them blew themselves up near the headquarters of state security and military intelligence," Syrian Observatory for Human Rights director Rami Abdel Rahman told AFP.
He said a senior intelligence officer was among the dead in the twin attacks in the heavily guarded Ghouta and Mahatta neighbourhoods.
Security forces locked down the city centre.
Homs has been under the full control of the government since May 2014 when rebels withdrew from the centre under a UN-brokered truce deal.
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State television paid tribute to the "martyrs" in the latest bombings.
There was no immediate claim for the bombings but they bore the hallmarks of the Islamic State group, which controls swathes of the largely desert countryside east of Homs.
Government forces retook the oasis city of Palmyra and its UNESCO-listed ancient ruins in a much heralded Russian-backed offensive in March last year but were then pushed out by IS in December.
Since then, the focus of government efforts has been further north, on second city Aleppo, which they fully retook after a rebel withdrawal in December, and areas to its east and west.
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