The 79-year-old man was approached by the dog at around 2.30pm on Monday 4 April while walking in Ellis playing fields off Healds Road.
The dog, which was off the lead, bit the man on his torso and leg before the owner got hold of the animal and left the scene.
The victim later had hospital treatment for his wounds.
Police say a number of enquiries have been ongoing to identify the owner who is described as around 5ft 8in tall, scruffy and dressed in a tracksuit, trainers and hooded top with the hood up. The dog was described as a bulldog type animal.
Anyone who saw the incident or who recognises the description of the animal and owner, is asked to call Dewsbury NPT on 101.