Osimhen’s three goals against Teramo took his tally to six in two pre-season friendlies for Napoli.
The 21-year-old just joined the Serie A side last month from Lille for €80m deal.
The Nigerian international had grabbed a debut hat-trick for his club last week as Napoli demolished L’Aquila 11-0 in a pre-season friendly.
Osimhen netted an early first goal for Napoli after just four minutes into the game before Hirving Lozano doubled the lead for Gennaro Gattuso’s men.
The attacker then scored two goals in the second half of the encounter to give Napoli the victory against Teramo.
He was later substituted in the 75th minute for Fernando Llorente.
Osimhen is expected to make his first Serie A appearance against Parma on September 20 after the Italian league fixture for the 2020/21 season was released on Wednesday.