The blasts, one from a car bomb and another from a suicide attack, struck the Zahra district in the middle of the city, said the so-called Syrian Observatory for Human Rights (SOHR), a Britain-based group close to Syria's foreign-backed opposition.
Syria's state news agency SANA reported two car bomb blasts, but gave a lower initial toll of six dead and 37 wounded, Reuters reported.
It was the second major attack in the city since a ceasefire deal took effect earlier this month, paving the way for the government to take over the last terrorist-controlled area of Homs.
Twin blasts on Dec. 12, also in Zahra, killed at least 16 people. Islamic State in Iraq and the Levant (ISIL) claimed responsibility for that attack, saying it had detonated a suicide car bomb.
Under the Homs ceasefire deal, at least 700 militants and members of their families left the last terrorist-controlled area of the city, al Waer district. The United Nations presided over implementation of the deal.