The robbery happened on Friday, November 25 at around 7.20pm when three men forced their way into the victim's flat near Broadlea Grove, Bramley.
They threatened the 72-year-old man with a hammer and knife and demanded cash before searching the flat and stealing money he had saved.
The burglars also stole an Acer laptop, Motorola mobile phone, packets of tobacco and two bottles of Irish cream liqueur.
The victim has an existing heart condition and was taken to hospital following the incident, where he remained over the weekend before being discharged.
They left in a dark-coloured hatchback car, similar to a new Ford Fiesta, in the direction of Broadlea Hill.
Police have today (Friday) released CCTV images of the suspects and appealed for witnesses to come forward.
Detective Constable Nick Dodsworth, of Leeds District Crime Team, said: "This was such a distressing ordeal for the victim that he was taken ill and had to be treated in hospital over the weekend.
"We believe these individuals have deliberately targeted him and we are keen to hear from anyone who has seen them or the vehicle in the area or who has any information that could assist the investigation."
The driver of the car is described as white, about 5ft 5ins tall, stocky, and either bald or with very light coloured hair.
He was wearing a light-coloured nylon top and tracksuit bottoms.
A second man is described as white, slim, about 5ft 7ins tall, aged about 22-years-old, with dark hair that was shorter at the sides and combed over on top.
He was wearing a black jumper and a body-warmer that had a thick navy blue band at to the bottom.
The third man was described as white, skinny, about 5ft 5ins tall, aged about 22-years-old, with mousy brown hair.
He was wearing a black padded jacket with lots of zips and grey jogging bottoms.
Anyone with information is asked to contact DC 1319 Dodsworth at Elland Road via 101 quoting crime number 13160706096 or call the independent charity Crimestoppers anonymously on 0800 555 111.