Peter Davies, 71, has told a judge he created the design when he was a teenage schoolboy.
He has made a copyright complaint and wants damages but bosses at the Premier League club dispute his claim.
They said he has no original artwork, has waited too long to launch legal proceedings and his claim should be dismissed.
Mr Justice Nugee is analysing the case at a High Court in London.
It is due to end next week.
Mr Davies, who comes from Wolverhampton but but now lives in Stourport, said he drew the wolf head logo at school in the early 1960s and entered it in a competition run by a Wolverhampton art gallery.
He said he composed sketches after a teacher asked him to demonstrate an understanding of Blaise Pascal's Hexagrammum Mysticum Theorem.
Mr Davies, a former building industry manager, said he recognised the drawing in 1979 when he noticed Wolves' new kit bore a wolf head logo.
The judge has heard he applied to register a wolf head design in 2016.
Mr Davies said his original artwork was never returned and there were reasons for his "long delay" in bringing proceedings.
He said he wrote to the club in 1979 complaining about the use of his design but received no response and did not pursue the matter at that time.
Mr Davies said the delay should not "extinguish" his rights.
Club bosses said the 1979 logo was designed by graphic designer Ian Jackson and "revamped" by designer Jonathan Russell in 2002.
They said there was no reason why either designer would have copied Mr Davies' "alleged design".
Bosses said the "very long delay" in launching proceedings should count against Mr Davies.
They said he has "no real excuse" for failing to bring the claim sooner.