A jury, which deliberated for almost five days, backed Apple's claim that Samsung had copied some of its technology used to power the iPhone.
It's the latest verdict in a legal battle that began in 2011. Initially, Apple was seeking $2.5bn (£1.87bn) but was awarded about $1bn (£750m) by a jury in 2012.
An appeal court determined Apple could not legally lay claim to the iPhone's appearance. That meant Samsung was asked to pay about $548m (£328m).
Samsung believes it should only need to pay $28m (£21m) for the parts it has used and not damages equivalent to the profits from the iPhone.