Gordon Culliford, 77, from Ammanford, Carmarthenshire, was last seen at about 13.15 BST on Thursday at the city's Singleton Hospital.
He is white, 5ft 7in tall, with white swept back hair and was last seen wearing black glasses and a red jacket.
South Wales Police said there is "considerable concern" for the man and called or information.

A spending timeline until 2022 shows the price could be about £435,000 more than approved in the Scottish Borders authority's budget earlier this month.
The Scottish government contribution to the project has been estimated at about £32.5m.
The council is being asked to approve the final outline design of the scheme and aim to publish it in April.
A report to the local authority described publication as "the most important stage of the project for determining the programme and successfully obtaining funding".
It warned that if the objection resolution process went beyond an estimate of three months, it could put funding at risk as well as the delivery target of June 2021.
However, the project team has tried to avoid that prospect with extensive consultation over the past two years.
A search has been launched for a pensioner who has gone missing in Swansea.
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A council report has shown the total estimated costs of a flood protection scheme for Hawick could top £41m.