Arsene Wenger's side last won the league in 2004 and have been without a trophy in the last eight years.
Last term, Arsenal had secured just five league wins by the start of December which put them 12 points behind league leaders Manchester United, but Giroud has backed Arsenal to be a bigger threat next season.
|12/1||Arsenal are 12/1 with Coral to win the Premier League
"We have also improved as individuals throughout the season, especially the newcomers like Santi [Cazorla], Lukas [Podolski] and me.
"It is a massively important season with a lot of challenges.
"I also want to really establish myself with Arsenal and make a name for myself here."
Giroud arrived from Montpellier last summer and scored 17 goals in all competitions for Wenger's side in his debut campaign.
The France international insists he never considered himself as a replacement for Robin van Persie, who departed the club for Manchester United, and says consistent selection will get the best out of him next season.
"It was not easy [to come to the club after Van Persie] at all," he said.
"It was a massive challenge with a positive pressure. I arrived here in a very humble way. I never said I wanted to replace Robin. He needed a few seasons to really be at his best here.
"I hope that as early as my second season, I can play week in week out and keep scoring regularly because it’s key for a striker."