Lieutenant-Colonel Paul Atterbury, the prosecutor, said in his opening statement that Grayson lied to investigators to help cover up the killings.
But Grayson's defence lawyer said the officer had no motive to lie about the killings because he was not present when they happened.
"Lieutenant Grayson is nothing more than a fall guy in a botched investigation under intense media pressure," Major William Santmyer told the jury of seven officers.
If found guilty, Grayson faces a maximum of 25 years in prison, forfeiture of all pay and dismissal from the Marine Corps.
Atterbury told jurors there are key undisputed facts in the case: A roadside bomb killed a marine and wounded two others and two hours later the squad's actions resulted in the deaths of 24 Iraqis.
Initially four marines were charged with murder.
However, the charges against three marines were later dropped, and charges against the fourth, Staff Sergeant Frank Wuterich, were reduced.
In addition, four commissioned officers were accused of failing to investigate the case or covering up the incident, but charges remain against two: Grayson and Lieutenant-Colonel Jeffrey Chessani, a battalion commander.
Investigators say Wuterich and a squad member shot five men by a car after the bombing.
Wuterich then allegedly ordered his squad into several houses, where they cleared rooms with grenades and gunfire, killing unarmed civilians.
Grayson was not present at the scene of the killings, but is accused of telling a sergeant to delete photographs of the dead from his digital camera.
Santmyer said the only connection between Grayson and the Haditha case are pictures.
"What the evidence will not show and what the government will not be able to show is a motive for the misconduct Grayson is alleged to have committed,'" he said.
Grayson is charged with making false official statements, trying to fraudulently separate from service, attempt to deceive by making false statements and obstruction of justice by trying to impede an investigation.
Grayson, who says he did nothing wrong, rejected a plea deal under which his charges would have been dismissed in exchange for an admission that he covered up the killings, his lawyer has said.
Wuterich faces voluntary manslaughter and other charges. Chessani is charged with dereliction of duty and violation of a lawful order on allegations he mishandled the aftermath of the shooting deaths.