Two men have been arrested on suspicion of murder following the death at Rosgill Drive, Seacroft.
Police were called to the scene at about 4.36pm today in response to a report of a man with a gun.
Armed officers attended the scene and found a man with a head injury. A gun was also recovered.
A West Yorkshire Police spokesman said: "Emergency services treated the injured man at the scene, but he was sadly pronounced dead a short time later.
"Following enquiries at the scene two men were arrested on suspicion of murder.
"Enquiries into this incident are still at an early stage, although it is not thought to have involved a firearms discharge."
Anyone who can help the police investigation is asked to call 101, quoting log 1604 of 1 January.
Information can also be reported anonymously to the independent charity Crimestoppers on 0800 555111.