Her hearing comes with tensions soaring between Moscow and Washington over Russia's military intervention in Ukraine that has sparked international condemnation and a litany of Western sanctions.
Griner's trial has accelerated in recent days as the United States and Russia discuss a potential prisoner swap that could involve the basketball star.
The court could announce its verdict as early as Thursday, the athlete's legal team told AFP.
"I ask the court to find Griner guilty and sentence her to nine years and six months in prison," prosecutor Nikolay Vlasenko said, requesting a term just short of the maximum punishment of 10 years.
He also requested a fine of one million rubles ($16,590) for the 31-year-old athlete, AFP heard in the court in the town of Khimki just outside Moscow.
Griner has been charged with drug smuggling for possessing vape cartridges with cannabis oil that were found in her luggage at a Moscow airport.
Vlasenko said Griner "deliberately" proceeded through the green corridor at customs and stated she had nothing to declare "in order to conceal" the substance.
Griner walked into the courtroom in handcuffs, escorted by several law enforcement officers and a police dog.
Standing inside a cage for defendants before the start of the hearing, she held up a photo of herself with teammates from the Russian club she plays for.
Her lawyer Maria Blagovolina told the court Griner was "an icon for many people" and "was brave" to admit her guilt.
She added that the amount of substance brought in by the athlete was "just over" the allowed amount.
Blagovolina asked the court to acquit Griner or consider a more lenient sentence if she is found guilty.
The two-time Olympic basketball gold medallist and Women's NBA champion was detained in February, just days before Moscow launched its military intervention in Ukraine.
She was detained when she came to Russia to play club basketball with UMMC Ekaterinburg during the US off-season -- a common path for American stars seeking additional income.
Griner pleaded guilty to the charges, but said she did not intend to break the law or use the banned substance in Russia.
In previous hearings, Griner said she was regularly tested by US, Russian and European leagues.
The WNBA star said she had permission from a US doctor to use medicinal cannabis to relieve pain from her many injuries -- "from spine to cartilages."
Her case has raised speculation about a potential prisoner swap between Moscow and Washington.
US Secretary of State Antony Blinken said last week that Washington had made a "substantial proposal" to Moscow to free Griner and former US Marine Paul Whelan, who was imprisoned on espionage charges.
The swap was also discussed during a call between Blinken and his Russian counterpart Sergei Lavrov on Friday.
The highest-profile Russian prisoner in the United States is Victor Bout, a 55-year-old arms trafficker, dubbed the "Merchant of Death", who is serving 25 years in jail.
There is no official confirmation that Washington has offered to exchange him.
Russia and the United States have already conducted one prisoner swap since the start of Moscow's Ukraine offensive.
In April, Washington exchanged former US Marine Trevor Reed for convicted drug smuggler Konstantin Yaroshenko.