The postponement came after one of the victims injured in the shooting had died.
The defendant was identified as Wiwat Yodpasit, 24, and is charged with attempted murder and illegal possession of firearms and violation of the emergency decree. He has denied all charges.
The February 1 shooting occurred while protesters of the People's Democratic Reform Committee ( PDRC) were laying siege to a polling unit near the Laksi district office to prevent the election from being held. The PDRC protesters were met with resistance from pro-government residents.
A man armed with a gun hidden in a popcorn bag emerged at a protest at Lak Si intersection on February 1 and opened fire at random.
An elderly street vendor hit by a stray bullet during the incident died last month after more than seven months of paralysis.
The hearing has been postponed until January 19, 2015.