Born as the son of an egetano (constituent of Vélez-Blanco) street sweeper driver and a Catalan hairdresser, Albiol grew up in Morera, on the outskirts of the city of Badalona, and studied at the Colegio Badalonés.

In 2010, rival party Initiative for Catalonia Greens brought a case against Albiol before the Public Prosecutor's Office of Barcelona, charging him with violating article 510 of the Spanish Penal Code following his publication of a pamphlet they alleged to be xenophobic because it linked immigration of Romani people from Romania to increased crime.

Responding to the news, Albiol was quoted by El Mundo as saying "Esta ciudad está indignada al ver lo que se ha hecho hoy.

Por primera vez, en esta ciudad hay una alcaldesa que no es de la fuerza más votada."

)[6] In April 2020, Socialist mayor Àlex Pastor resigned after being arrested for assaulting a member of the Mossos d'Esquadra.

[7] In addition to his role in parliament, Albiol has been serving as member of the Spanish delegation to the Parliamentary Assembly of the Council of Europe since 2016.

In October 2021, Albiol's name appeared on the Pandora Papers linked to an offshore venture in Belize,[8] leading the opposition groups in the city council to announce a vote of no confidence against him, which was passed on November 8, 2021, and resulted in Rubén Guijarro of the Socialist Party of Catalonia replacing Albiol as mayor.