The drill, named Great Prophet 9, was held near the Strait of Hormuz, through which one fifth of the world's oil passes. Iran's regular army carried out naval drills near the strait in December.
State TV showed footage of missiles fired from the coast and the fast boats striking the mock U.S. Aircraft carrier.
The drills, which also included shooting down a drone and planting undersea mines, were the first to involve a replica of a US carrier.
Last month Fadavi said his force is capable of sinking American aircraft carriers in the event of war.
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The Guard's chief commander, Gen Mohammad Ali Jafari, said the drills send a "message of (Iran's) might" to "extraterritorial powers," a reference to the United States.
Cmdr Kevin Stephens, the spokesman for the US Navy's 5th Fleet in Bahrain, said the Iranian naval exercises began a few days ago and have had no effect on maritime traffic.
"We're quite confident of our naval forces' ability to defend themselves," he said. "It seems they've attempted to destroy the equivalent of a Hollywood movie set."
Iran is currently negotiating an agreement over its disputed nuclear program with the United States and five other world powers. The two sides hope to reach a framework agreement next month and a final deal in June.
Western nations have long suspected Iran is covertly seeking a nuclear weapons capability, charges denied by Tehran.