The man walked into Yorkshire Bank, in Town Street, Bramley, at about 4pm on Thursday and gave a female cashier a note demanding money. He then produced a silver handgun from his waistband.
She handed over money, the alarm was activated and he escaped.
But police believe someone will recognise him from CCTV images.
Detective Inspector Paul Hobson, of Leeds CID, said: “Although the man has attempted to disguise himself, the CCTV images paint a very distinctive picture of him and we would urgently like to hear from anyone who recognises him.
“The clothing he is wearing is also distinctive. He is wearing what appears to be a Lacoste woolly hat with the crocodile logo on it and a Sergio Tacchini jacket with the logo on the left chest.”
Anyone who thinks they know him should contact Det Con Andy Smurthwaite at Elland Road via 101 or call Crimestoppers, anonymously, on 0800 555111.