The construction of the Alexander Suvorov is to start July 28 - Russia's Navy Day, while another submarine, Mikhail Kutuzov, will be built in November.
Work on the two submarines have been underway since 2011.
One submarine of the same class, Knyaz Vladimir, has been under construction since July 2012, Xinhua said.
Russia plans to build eight submarines of that class until 2020 to form the core of its navy's nuclear deterrence strategy.
They will replace the Project 941 (Typhoon by NATO classification) and Project 667 submarines. Three of them will be of Borei and five of Borei A type.
The Borei class submarines are capable of carrying 16 new multiple-warhead Bulava ballistic missiles, while the Borei A submarines can carry 20.
The first Borei-class submarine, Yury Dolgoruky, was put into active service Jan 10 in the Northern Fleet. The second Borei submarine, Alexander Nevsky, is undergoing sea tests.
