Ford Motor Co. is facing a potential $1.7 billion in punitive damages after a Georgia jury reached a verdict Friday in a case involving a 2014 rollover of a Ford F-250 pickup truck that left two people dead.

The Gwinnett County jury determined that damages should be imposed on Ford for selling 5.2 million Super Duty trucks with what plaintiffs’ attorneys said were dangerously weak roofs that could crush passengers in a rollover accident, according to James Butler, a lawyer representing the plaintiffs in the case.

The case was brought by the family of a Georgia couple, Melvin and Voncile Hill, who were driving a 2002 Ford F-250 Super Duty truck from their farm when the right front tire blew out and the truck rolled over, Mr. Butler said. The Hills were crushed inside the truck, he added.

Ford Chief Executive Jim Farley said last month that the company continues to be hampered by recalls and customer-satisfaction actions.

Photo: Nic Antaya/EPA/Shutterstock

“While our sympathies go out to the Hill family, we don’t believe the verdict is supported by the evidence, and we plan to appeal,” a Ford spokesman said Saturday.

The $1.7 billion verdict is believed to be one of Georgia’s biggest in history and is unusually large for an accident-related lawsuit involving an auto manufacturer. Typically, damages in these types of cases run in the millions of dollars, and many are settled out of court. Often, high-dollar  verdicts are later reduced by judges or the appeals courts.

“The Hill family is glad this part of the case is finally over,” Mr. Butler said. “They intend to persevere and make Ford pay.”

On Thursday, the Georgia jury awarded plaintiffs Kim and Adam Hill, the children of the couple who died in the crash, $24 million in compensatory damages, Mr. Butler said. The jury allocated 70% of fault in the case to Ford, Mr. Butler said.

Ford executives have for years worked to tackle costly quality and warranty problems with their vehicles, including making this effort a priority under the current chief executive, Jim Farley. The company has issued 49 recalls this year, the most of any auto maker, according to data from the National Highway Traffic Safety Administration.

“We continue to be hampered by recalls and customer-satisfaction actions,” Mr. Farley said on a July earnings call. “This affects our cost but more importantly, it falls short on our most fundamental commitment to our customers.”

Last year, Ford set aside more than $4 billion for warranty costs, up 76% from five years earlier. The car company’s total warranty expenses increased about 17% from 2016 to 2021.

Earlier this year, Mr. Farley brought on a new executive director of quality, Josh Halliburton. Before coming to Ford, Mr. Halliburton spent 17 years at J.D. Power, an independent research firm that specializes in assessing and studying vehicle quality.

“We are placing more time and emphasis on ensuring everything is done right upfront to prevent quality issues from manifesting later in the development process,” Mr. Halliburton said.

He added that he expects to see Ford’s warranty problems improve next year, but that it might take two to three years to see results with the most impact.

Write to Nora Eckert at nora.eckert@wsj.com