The penalty is on top of $US4.1 million ($A5.9 million) in compensatory damages already awarded - for falsely claiming the shooting was a hoax.
Neil Heslin and Scarlett Lewis, separated parents of slain s-year-old Jesse Lewis, testified that followers of Jones harassed them and sent them death threats for years in the false belief that they were lying about their son's death in the December 14, 2012, shooting that killed 20 children and six staff at Sandy Hook Elementary School in Newtown, Connecticut.
The 12-person jury on Thursday decided on the compensatory damages following a two-week trial in the defamation lawsuit presided over by Judge Maya Guerra Gamble in state court in the Texas capital of Austin, where Jones' radio show and webcast Infowars are based.
The parents had sought $US145.9 million ($A211.1 million) in punitive damages and $US150 million ($A217 million) in compensatory damages. Compensatory damages are awarded to cover a plaintiff's suffering and losses. Punitive damages are awarded to punish a defendant's actions.
Jones, who has been a prominent figure in American right-wing circles and a supporter of former president Donald Trump, had called the Sandy Hook massacre a hoax by the US government staged using crisis actors to serve as a pretext for taking away Americans' guns.
"We ask that you send a very, very simple message, and that is: stop Alex Jones. Stop the monetisation of misinformation and lies," Wesley Todd Ball, a lawyer for the parents, told jurors earlier on Friday before they began deliberations on punitive damages.
The Sandy Hook gunman, Adam Lanza, used a Remington Bushmaster rifle to carry out the massacre. It ended when Lanza killed himself with the approaching sound of police sirens.
A lawyer for Jones, Federico Andino Reynal, asked jurors to return a verdict of $US270,000 ($A388,470) based on the number of hours Infowars devoted to Sandy Hook coverage.
Forensic economist Bernard Pettingill testified on Friday on behalf of Lewis' parents that Jones "promulgated some hate speech and some misinformation" and "made a lot of money." Jones and Infowars are worth between $US135 million ($A195 million) and $US270 million ($A391 million) combined, Pettingill said.
Jones sought to distance himself from the conspiracy theories during his testimony, apologising to the parents and acknowledging that Sandy Hook was "100 per cent real".
Jones' company, Free Speech Systems LLC, declared bankruptcy last week. Jones said during a Monday broadcast that the filing will help the company stay on the air while it appeals. The bankruptcy declaration paused a similar defamation suit by Sandy Hook parents in Connecticut where, as in Texas, he has already been found liable.
During closing arguments on Wednesday, Kyle Farrar, a lawyer for the parents, urged the jury to end what he called their nightmare and hold Jones accountable for profiting off their son's death.Â
Reynal acknowledged during his closing argument that Jones and Infowars reported "irresponsibly" on Sandy Hook but said his client was not responsible for the harassment.
The plaintiffs also have accused Jones of approaching the trial in bad faith, citing broadcasts in which he said the proceedings were rigged against him and that the jury pool was full of people who "don't know what planet they're on".
