The school, which has more than 700 students, opened in 2007. The students spend a substantial portion of their time working in creative intellectual laboratories.
The President saw an algebra lesson conducted using distance learning, with students at a school in Moscow taking part via internet.
Mr Medvedev also visited creative laboratory Studio TV5, where year seven students interviewed him for the school newspaper and television channel.
Later, the President spoke with year nine students about their future career choices.