[3] Gianluigi was born in Cittadella on 1 February 1996[4] and grew up in Porto San Giorgio with his mother Carlotta, a ski racer and handball player, and his father Luca, the president of a local tennis club.

[5] Initially Quinzi applied himself to Alpine skiing, gaining a second place in the championships of the Trentino-Alto Adige; but at seven years old, after leaving other sports as well, he focused his efforts primarily on tennis.

In March, Quinzi reached the final of the 43rd Banana Bowl tournament; he lost in three sets to the French player Jean Sebastien Tatlot.

With an outstanding performance Quinzi beat Kyle Edmund in straight sets to reach his first Junior Grand Slam final.

In September 2011, Quinzi obtained his first ATP point at the 2011 Mazatlán Open beating the Swiss tennis player Luca Margaroli in the first round.

His first best result in ITF Men's Circuit went in 2012 Pozzuoli, where he reached the quarterfinals, but he lost to the Italian player Alessio di Mauro.

On November 23, 2012, he reached is first ITF final in the tournament of Curico, Chile ($10,000, on clay court), defeating Juan Carlos Sáez (world rank No.

In 2013 Quinzi obtained his first big professional result in March: in the first ITF Futures tournament he took part, in Bogotá, he soon reached his second career final, beating high-ranked players than him.

He then received a wild card to enter the main draw of the 2013 Rai Open, the first clay court Challenger tournament of the season played in Italy, but he lost in the first round to former Top 100 player Frederico Gil in three sets.

In August Quinzi took part to two other Challenger tournaments in Italy but lost in the first round to Italian Top 100 players Filippo Volandri and Paolo Lorenzi.

In September Quinzi continued playing in ATP Challenger Tour, taking part to some tournaments in South America: at 2013 Quito Challenger Quinzi lost in the second round to eventual semifinalist Giovanni Lapentti; in Porto Alegre, one week later, he entered the main draw as a qualifier and stunned Gastão Elias (world rank No.

Quinzi then reached for the first time the quarterfinals round on an ATP Challenger Tour tournament, defeating Leonardo Kirche 6–2 6–2, but lost in three sets to Pedro Sousa.

In November, in Colombia, Quinzi beat again Gastão Elias with a stunning 6–2 6–0 to reach the second round of the 2013 Challenger Ciudad de Guayaquil where he overtook Bolivian player Hugo Dellien in straight sets.

In May, after the divorce from his coach Eduardo Medica, Quinzi obtained his best results in 2014, capturing three $10,000 ITF tournaments in three weeks – and winning 15 matches in a row: in Galați, Romania, he beat Romanian Vasile Antonescu, in Safi, Morocco, he beat Hugo Dellien 6–2, 6–2 (capturing the title without losing a set) and then in Casablanca he defeated Gianni Mina in straight sets.

At the end of January Quinzi took part at his first 2015 tournament in Palm Coast: playing on clay, the Italian reached the quarterfinals of the $10.000 ITF event, where he was defeated by eventual finalist Patricio Heras.

A couple of weeks later, Quinzi won his fifth Future tournament of his career, beating Federico Coria with the score of 6–4, 6–4 on the green clay of Sunrise (Florida).

After being awarded a wildcard thanks to a qualifying tournament, Quinzi took part in the first edition of the 2017 Next Generation ATP Finals, held in Milan, Italy.