His lawyers deny that he threw the grenade and contend that the prosecution is relying on confessions extracted following abuse.
His lawyers had argued that his statements to military interrogators were illegally obtained through torture and had asked a US war crimes court to throw them out.
Tuesday's trial began with jury selection from a pool of US military officers.
"Potential jurors were asked if they had previous knowledge of the case? If they had any formed opinion about Guantanamo Bay and the way this base and prison has been run?" Al Jazeera's Monica Villamizar said, reporting from Guantanamo Bay on Tuesday.
"The defence lawyer asked if jurors had any type prejudice towards Muslims.
He even asked the specific question: if they ever sat next to a Muslim on an air plane, if the thought ever crossed their mind that this person was going to take over the flight?" our correspondent said.
Opening arguments are planned for Wednesday, with the trial expected to last roughly three weeks.
US forces captured Khadr, 23, in Afghanistan in July 2002, when he was just 15 years old.
Khadr, who has refused a plea deal, faces a maximum life sentence if convicted.
"Omar Khadr could potentially be the first child soldier to be prosecuted for war crimes in modern history," our correspondent said.
"Under international law, children captured in war should be treated as victims and not perpetrators."
In a rare interview, Zeynab Khadr, Omar's sister, told Al Jazeera that she still sees Omar "as her younger brother".
Zeynab said her family did not have an unusual life, but her and Omar did play with Osama bin Laden's children in Afghanistan.
Khadr's case is the first to go to trial under the system of military commissions for detainees captured by US forces in a global campaign following the September 11, 2001, attacks on the US.
Obama had sought to close the detention centre that has been the object of international condemnation, but he has faced congressional opposition on transferring the detainees to US soil.
The president has introduced some changes designed to extend more legal protections to detainees, but the tribunals' long-term future remains uncertain.
But Navy Captain David Iglesias, a lawyer and spokesman for the military commission's prosecutors at Guantanamo Bay, told Al Jazeera that the tribunals have improved and that Khadr can get a fair trial.
"It is a case that has been pending for many, many years," he said.
"The government is ready to go forward. To what extent it has international repercussions is beyond anybody's guess.
"The Military Commissions Act has been revised. It is a much better law than what it was under the 2006 Act.
"I believe based on my experience it is a fair system."
Our correspondent said that Khadr's attitude has changed drastically since his first court appearance in 2006.
|Obama is facing legal and political obstacles in trying to shut down Guantanamo Bay
"He was very co-operative with the military system [but] now it is completely different," she said.
"Khadr's lawyer told me recently that he is trying to convince [Khadr] to be co-operative: to show up in trial and not [to] fire his only military defence lawyer who was assigned to him.
"Khadr has expressed in the past that he want[s] to be convicted, [to] show the world how unfair this system is ... and to show that the US will eventually convict child soldiers."
In a letter to Dennis Edney, his Canadian lawyer, published in newspapers in Canada and the US, Khadr said the trial may show the world how unfair the process is.
"The world doesn't get it, so it might work if the world sees the US sentencing a child to life in prison, it might show the world how unfair and sham this process is," Khadr said.
"And if the world doesn't see all this, to what world am I being released to? A world of hate ... and discrimination."
Separately on Tuesday, the Pentagon is also preparing to hold a military commission for the sentencing of Ibrahim Ahmed Mahmoud al-Qosi, a Sudanese detainee at Guantanamo.
Al-Qosi is accused of acting as accountant and aide to Osama bin Laden, the al-Qaeda chief, in the 1990s when the network was centred in Sudan and Afghanistan.
He is also accused of later working as bin Laden's bodyguard.
Al-Qosi pleaded guilty last month to one count each of conspiracy and providing material support to terrorism as part of a plea deal with prosecutors.
The 50-year-old had faced a potential life sentence if convicted at trial.
On Monday, a US military judge ordered that the plea deal, which put a cap on al-Qosi's sentence, be sealed.
The judge, Air Force Lieutenant Colonel Nancy Paul, said the deal limiting how much more time detainee al-Qosi spends in confinement will not be revealed until after his release.
She said that condition of the plea bargain was requested by the government and agreed to by the detainee's lawyers.
A jury of military officers is expected to begin deliberating al-Qosi's sentence on Tuesday, but officials overseeing the tribunals will reject their decision if it exceeds the terms of the plea bargain.
A longer sentence could be applied, however, if al-Qosi did something to break the terms of the plea agreement.