But Paul Sutton, its new headteacher, said the school needs more time to prove itself.
Mr Sutton, who is just eight weeks into the job, is the academy's third head since it opened two years ago. The first was inexperienced, said Mr Sutton, and inherited the problems of the failing school it replaced, St David and St Katherine's.
Within six months the Department for Education and Skills sent in a troubleshooting team on an 18-month contract to ensure that its first academy was not a failure.
Even now, despite a pound;12 million investment, the buildings are not finished because of slow progress on the cramped inner-city site.
Greig has 800 pupils, 100 below capacity, but Mr Sutton said Year 7 and 8 places were being filled, which was a vote of confidence. When work is complete, the school will be able to cater for 1,200.
He said: "The academy's reputation is based on a perception of its history and a lack of current knowledge. The offer extended to everyone is to come and see us: the reality of what's going on is miles away from the reputation."
His experience turning around another former failing school in a neighbouring borough tells him not to panic because parents will eventually be won around.
Mr Sutton said: "You can't put in a new head and change everything in a term. The pupils are still the same. But I have been very impressed with their commitment to improving their reputation and their own image. That's the key to their long-term success and that's why I took the job."