The former Northampton Town frontman rejoined the Gills on Wednesday, having previously played for the Kent club during the 2010-11 season.
Akinfenwa believes that Martin Allen's side could challenge for a top-half finish, a year after winning promotion from League Two.
"I sat down with the chairman and the gaffer, I've trained with the boys and there is really good ability and youngsters coming through and I don't think you should go in to any season not thinking you're going to do well," Akinfenwa told Gillingham's official website.
"It's a realistic aim to hit the playoffs or get promoted but it's a long season and we are equipping ourselves well and we feel confident.
"There is a real togetherness and team spirit and you need that because there will be ups and downs but I think we'll do well."
Gillingham finished top of League Two last season.