The card, dated September 25 1986, dropped through the letterbox of Gethin Davies from Bonymaen.
Bearing two 1980s Spanish stamps and a British second-class stamp, it was sent by someone called Phyl, to a Mrs E Leon.
Mr Davies now hopes to reunite it with the person it was intended for.
In his postcard, Phyl writes that the weather is nice, he has a self-catering apartment near a pond, but complains about the "expensive" cost of Spanish bread at Â£1 a loaf.
Although it was delivered to the right address on the card, Mr Davies said he has no clue who either Phyl or Mrs Leon could be.
"I've been baffled by it really," he said.
"I suppose Mrs Leon once lived in my flat, but I've asked around neighbours who have lived here 20 or 30 years, and none of them have ever heard of her.
"The Post Office say they have no idea what could have happened to the postcard for 29 years, may be it got stuck in a sorting machine, may be given that it's got both British and Spanish stamps on it, someone found it and posted it on.
"Really I'd just like to find out who either Phyl or Mrs Leon are, so I could finally give it to them after all this time."

Duns, Hawick, Peebles and Selkirk saw numbers rise with a regionwide increase of 1% last year compared with 2015.
There was a drop in footfall recorded in Galashiels, Jedburgh, Kelso and Melrose.
Eyemouth - which has only been included in the figures for the past five years - also saw its figures decline compared with last year.
Stuart Bell, executive member for economic development on Scottish Borders Council, said the results painted a "very mixed picture".
However, he said it was good to see a "substantial increase" in Hawick where the council was working with a range of partners on an action plan to boost the town's economic fortunes.
"The co-operation of local community groups and businesses is a key element of that work, and particularly so in areas around tourism and positive promotion of the town, which would hopefully drive even more people to visit," he said.
"The recently-established town centre resilience index uses a range of statistics, including footfall and retail vacancies, to help us target council resources for maximum impact in the towns in greatest need.
"These latest figures confirm that we must extend our efforts in Jedburgh and Eyemouth to help their economies."
Ron Smith, executive member for planning and environment, said the results, when read with other indicators showed "consolidation" which he said was positive in itself in "tough economic times".
"However, there are certainly indications that some of our town centres are struggling, particularly Jedburgh with a further fall in footfall and an increase in vacant shops, and we are already investigating steps to address such issues," he said.
"The council alone cannot revive our high streets and our partners, community groups, businesses themselves and the public have a role to play in ensuring that bustling Borders towns are not a thing of the past.
"On a personal note, I must welcome the improvement in the figures for Hawick, which brings with it an optimism that a corner may be turning."
A Swansea man has been left scratching his head after receiving a postcard from Spain 29 years after it was sent.
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A town centre footfall study across eight main Borders towns has recorded its highest figures since 2012.