Iran grabbed one gold, one silver and five bronze medals in the competition and finished in second place with 130 points.
Host Russia won the title with 183 points and Azerbaijan came third with 101 points.
Amirreza Dehbozorgi won a gold after beating Alimardon Abdulaef from Uzbekistan 3-1 in the 55kg final bout.
Saeid Esmaeili lost to Dinislam Bammatov from Russia 7-3 in 60kg final bout and snatched a silver medal.
Iman Mohammadi defeated Romanian Manuel Stoica 9-0 in the 63kg bronze medal match.
Mohammadhossein Azarmdokht beat Egyptian Emad Abouelatta 8-4 in the bronze medal match of 77kg.
Mohammadaziz Naghousi emerged victorious over Ukraine’s Mykyta Alieksieiev 11-5 in the 82kg and won the bronze medal.
Morteza Alghosi defeated Marcus Worren from Norway 5-3 in the 97kg bronze medal match.
And Amirmohammad Bayat defeated Nikolaos Ntounias from Greece 6-3 in the 130kg and seized a bronze.