Palou began his motorsport career in karting in 2003 , where he remained active until 2014. In 2006 he became Spanish champion in the Alevin class, in 2011 and 2012 in the KF3 class and in 2013 in the KZ2 class. In 2012 he won the WSK Euro Series in the KF3 class. In the 2012 CIK-FIA European Championship he came second in the KF3 class. In 2014, Palou made his debut in formula racing . For Campos Racing he started in the Euroformula Open . Palou won his first race in formula racing and scored two more victories over the course of the season. With eleven podium finishes, he finished the season in third place overall. He also took part in an event of the BRDC F4 Championship for Sean Walkinshaw Racing .
In 2015 , Palou stayed with Campos Racing and competed for the team in the GP3 series . He won a race and was tenth overall as the best driver in his racing team. He also took part in a North European Formula Renault race for Inter Europol . In 2016 , Palou completed his second GP3 season for Campos Racing. With a second place as the best result, he finished the season in 15th place overall.
After a test drive in Mid-Ohio in July 2019, he is expected to drive a car used by Dale Coyne Racing and Team Goh in the IndyCar Series in 2020 .