The card addressed to Steve Padgett included a handwritten message to someone called Gerry and was posted on 27 August 1981.
Samantha Williams, who received the card featuring a photo of the Sydney Opera House at her address in Elm Grove, Westgate, said the postcard was a “mystery.”
Ms Williams and her family assumed it was a Christmas card before inspecting it closely.
She told the BBC: "It had been sent from a man called Gerry in Sydney and addressed to Steve Padgett or Padge, who we believe lived here with his parents in the 1980s.”
She added: "We would love to find the man it was addressed to and give it to him. They were obviously good friends and it may mean a lot to him."
A Royal Mail spokeswoman told the BBC: "It is difficult to speculate what may have happened to this item of mail, but it is likely that it was put back into the postal system by someone recently, rather than it being lost or stuck somewhere.
"Royal Mail regularly checks all its delivery offices and clears its processing machines daily.
"Once an item is in the postal system then it will be delivered to the address on the card."
A similar situation occurred earlier this year in May, when a school in Shropshire, received a postcard that was sent 66 years prior. The letter was addressed to a Miss D Kerr believed to be a student at Adcote School at the time, from her mother.
The stamp revealed the original date to be 1957.