Hiroyuki Muramoto, 43, of the Thomson Reuters news agency, was shot in the chest by an unknown gunman on April 10, 2010 while covering clashes between Thai troops and the anti-government Red Shirts.
His brother told the hearing at the Criminal Court in Bangkok that he discovered Muramoto had been killed that evening on a website.
"Our family still wants to know who did it," he told the court through a translator.
Nobody has been charged with Muramoto's death and no suspect has been named.
The inquest is expected to take months to complete as prosecutors want to question dozens of witnesses to establish the circumstances of the death. The next session is scheduled for July 2.
More than 90 people, mostly civilians, were killed and nearly 1,900 were wounded during the two months of rallies, which drew about 100,000 Red Shirts at their peak, calling for immediate elections.
The kingdom, which remains deeply divided by the 2010 bloodshed, now has a new government allied to the Red Shirts' hero, fugitive former leader Thaksin Shinawatra, whose sister Yingluck is prime minister.
No soldier or official has been prosecuted in connection with the deaths during the unrest, prompting anger from relatives and rights groups who say those responsible are being protected by a culture of impunity in Thailand.
Police initially insisted that the military was not behind the killing of Muramoto, but Yingluck's government said in November there was clear evidence that soldiers were responsible.
In March this year Yingluck offered $250,000 in compensation to Muramoto's family.
A Thai court will open an inquest in July into the death of Italian freelance photographer Fabio Polenghi who was also killed while covering the 2010 unrest.