The French striker scored 17 times in all competitions in his debut campaign - second only to Theo Walcott in the Club's scoring charts.
Giroud has notched up six goals in three games on the Asia Tour and Rosicky expects an improvement now he has fully adapted to life in the Premier League.
I expect him to have a better season than he did last year, and I believe he can score more than he did then. If he continues with how he has played in pre-season, then why not?Tomas Rosicky
"When you come to England it can be difficult in the first season because you have to settle and get used to it," the Czech midfielder said.
"So I expect him to have a better season than he did last year, and I believe he can score more than he did then. If he continues with how he has played in pre-season, then why not?"
Rosicky - who sent in the cross for the Giroud's headed goal against Nagoya Grampus on Monday - believes that the striker's good form in Asia bodes well for the coming campaign.
"Well it is only pre-season, and even though we won the games, it doesn't mean much," he said. "But on the other side, goals always give strikers confidence, whenever they score them. Olly started very well and we know he has great qualities which he showed last season."Copyright 2013 The Arsenal Football Club plc. Permission to use quotations from this article is granted subject to appropriate credit being given to www.arsenal.com as the source 25 Jul 2013