The Staffordshire bull terrier type animal set upon the dog, which was being walked along with another dog by its owner.
The injured dog needed surgery and stitches for facial cuts, and officers are now trying to trace the owner of the black and brown fleck Staffordshire bull terrier type, which had a blue collar and chain lead.
It happened on Lickhill Road, Stourport-on-Severn, just before 7pm last Friday.
The man police are trying to trace was white, in his mid 70s, of large build with grey hair.
He was wearing a cardigan and black or grey trousers.
A spokesman from the Warwickshire Police and West Mercia Police dog unit said: "This was a very upsetting incident for everyone involved.
"It is believed that a woman had been in the area and witnessed the incident, and has yet to come forward.
"I would urge anyone who witnessed it, or has any information about the offending dog, to call 101, so we can speak to its owner.
"Alternatively you can contact Crimestoppers anonymously on 0800 555111 or via their website, quoting incident 755S of 25 August 2017.