Giroud, who joined Arsenal in the last transfer window is yet to score and had come under a lot of criticism by both the media and some fans.
Vermaelen thinks it's unfair to expect too much from the new boy at this time as he had played only three games.
“I’m convinced Olivier will be off the mark soon. It’s not as if he has had an easy start - he didn’t get much time against Sunderland, and then played in two tough away games.
“He won a lot of duels in those matches, and it’s a vital quality when you’re away from home - if we don’t see a solution, we can sometimes play a longer ball to him in the knowledge that he works hard and is strong in the air.
“He’s made some good runs and has been a bit unfortunate not to score so far, but he’s got into the positions so I’m not worried about him at all. The goals will come.”
Ahead of today's game against Southampton, Vermaelen wants the team to continue their good run, which he believes is down to their hardwork at the training ground.
“ I think you can see, particularly from the away games at Stoke and Liverpool, that the whole team - not just the defence, but every area - is working really hard at shape and organisation,” he said.
“It’s one of the main aspects of football, and we’ve been putting a lot of effort into getting it right.”