Huber made his international debut on March 1, 2008 at a junior competition in Bois-d'Amont and finished in 19th place. At the end of 2008 he made his debut in the Alpencup in Seefeld in Tirol and finished 48th and 35th. On February 1st, 2009 he made his FIS Cup debut in Eisenerz , but just finished 34th and missed the second round. Afterwards Huber competed in several junior competitions this season. In summer 2009 he competed in several FIS Cups. His best result was a 20th place in Val di Fiemme . This season, Huber started in all twelve Alpine Cup competitions. However, he only made it into the top ten in Seefeld in ninth place. In the winter, Huber started again in the FIS Cup in Lauscha and was 19th twice. Huber also competed in the FIS Cup in Villach , but could not reach the second round in 46th place. For the 2010/11 season Huber was nominated for the Austrian C-team. In summer, however, he only jumped in the Alpine Cup, until January also in winter. At the end of January Huber made his debut in the Continental Cup in Bischofshofen and was 39th and 49th. In February Huber made his breakthrough in Kranj . First he finished fifth and ninth in the FIS Cup. A week later, he made it onto the podium for the first time in third and second place in the Alpine Cup. He then reached the second round at the Continental Cup in Kranj on February 19 and 20, finishing eighth and eleven for the first time. He succeeded again a week later in Zakopane . He achieved his best results to date in the Continental Cup with two seventh places on July 2, 2011 in Kranj and July 10, 2011 in Stams . At the Alpine Cup in Chaux-Neuve , Huber jumped on the podium again in third place. For the 2011/12 season he was nominated for the B-team.
Huber started in the Alpine and FIS Cups at the same time until 2013, as there were no great successes in the Continental Cup. At the Winter Universiade 2013 in Predazzo , he won the bronze medal with the team. Just a few days after the Universiade, Huber moved permanently to the B national team and was able to celebrate his first two podium finishes in the Continental Cup in February 2014 with two third places in Brotterode .
After Huber achieved good results in the Continental Cup competitions from January 22nd to 24th, 2016 in Sapporo with places 15, 4 and 16, he was also part of the Austrian team for the World Cup competitions a week later at the same location. He made his World Cup debut on January 31, 2016, but with 35th place he missed the points. This remained his only World Cup station in the 2015/16 season. On February 27, 2016, he achieved his best placement in a COC class with second place in Brotterode. After two further podium finishes in the Continental Cup in the 2016/17 season, he scored his first victory in this series on December 28, 2016 in Engelberg . In the subsequent Four Hills Tournament in 2016/17 he only belonged to the national group in Innsbruck . With 30th place in the competition, he got the first World Cup point of his career. Despite further appearances in the World Cup, this one point remained in the overall ranking of the 2016/17 season .
In the summer of 2017, he was part of the Austrian team for the first time in a team competition in Wisła as part of the Grand Prix, with the team taking fifth place. In the further course of the summer he achieved three podium finishes in the Continental Cup , including a win on September 10, 2017 in Stams . The following winter , Huber was a permanent member of the Austrian World Cup team. At the start in Wisła, he jumped to second place in his first World Cup team competition and thus achieved his first podium finish in the World Cup. In the individual competition the following day, he finished sixth and improved his best position in an individual World Cup competition significantly (previously 30). On January 27, 2018, he scored his third victory in a Continental Cup competition in Sapporo . In the rest of the 2017/18 World Cup season, he regularly jumped into the points, but could no longer achieve his top placement from the start in Wisła. He finished the season 28th in the overall World Cup with 117 points.
On August 11, 2018, Huber achieved a podium finish in a Grand Prix competition for the first time in Courchevel, second behind Yevgeny Klimov . In addition, he took sixth and third place in the two competitions in Hakuba . In the final competition in Hinzenbach , he won his first Grand Prix jumping ahead of Killian Peier and Karl Geiger . In the Grand Prix overall standings, he was fifth with 305 points. On December 15, 2018, Huber achieved his first individual World Cup podium in Engelberg in third place. At the 2019 World Championships in Seefeld in Tirol , he and his teammates Philipp Aschenwald , Michael Hayböck and Stefan Kraft won the silver medal in team jumping. In the two individual competitions, he finished eleven on the large hill and 21 on the normal hill.