The Gunners ended a poor campaign on a high last season, finishing strongly to secure fourth place ahead of Tottenham and with it another shot at the Champions League.
Giroud believes if Arsene Wenger's men can hit the ground running in August they will be able to take the challenge to the likes of Manchester United, Manchester City and Chelsea.
"If we start better than we did this season, I know that we will compete for the title next year because we are used to playing together now and have improved as a team," Giroud told the Arsenal magazine.
"We have also improved as individuals throughout the season, especially the newcomers like Santi (Cazorla), Lukas (Podolski) and me."
Giroud joined Arsenal from Montpellier last summer and took some time to settle in before going on to become a focal point of the attack, finishing the season with 17 goals.
The 26-year-old feels next season can be even better on a personal level.
"It was not easy at all. It was a massive challenge," he said.
"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."
Giroud, who missed three of the Gunners' final four matches after his red card at Fulham, added: "I have scored fewer compared to last season in Montpellier but the ratio, minutes played to goals scored, is good."