Police received a report at 2.17pm on Tuesday that the man had been taken to hospital after being bitten by the Alsatian-type dog on Mill Lane, South Kirkby.
The other attacks happened on Mill Close and Holmsley Avenue last week and thought to be committed by the same dog.
The council dog warden was notified and both the police and dog warden made an extensive area search, with a number of addresses checked, but the dog was not located.
The police are reassuring residents that they are doing all they can to catch the animal.
Inspector Nick Drinkall, of Wakefield District Patrol Team, said: “We understand that these incidents are causing concern in the local community and I would like to reassure residents that we are working with the dog warden to locate this dog and identify its owner.
“If anyone believes they have seen this dog they are urged to report this to us as soon as they can.
“We will not tolerate people allowing their dogs to be dangerously out of control and will take action.”
A seven-year-old boy needed urgent surgery after the dog attacked him as he played in a friend's garden on Holmsley Avenue last Wednesday April 20.
After they were able to free the child, the dog ran off and attacked a 62-year-old man on Mill Close minutes later.
Anyone with any information about either of these incidents or the dog involved are asked to contact police by either calling 101 or using 101 Live Chat on the West Yorkshire Police website quoting crime reference 13220211431.