As a member of the Union of the Democratic Centre and later the Spanish Socialist Workers' Party (PSOE), he was a city councillor in Zaragoza from 1979 to 1995, serving as mayor since 1986.
Born in Tétouan, Spanish Protectorate of Morocco, González Triviño became mayor of Zaragoza in January 1986 after the death of Ramón Sainz de Varanda.
He oversaw the building of the Pabellón Príncipe Felipe sporting arena and the Auditorio, as well as remodelling of the plazas outside the Cathedral-Basilica of Our Lady of the Pillar and the Cathedral of the Savior of Zaragoza.
[3] After being defeated by Luisa Fernanda Rudi of the People's Party (PP) in the 1995 election, he concentrated on his seat in the European Parliament, won the previous year.
[6] In 2008, incumbent mayor Juan Alberto Belloch gave Zaragoza's gold medal to all of his living predecessors, including González Triviño.