Ian Collinson, 73, who wears glasses and walks with a stick, was seen on High Street, Micklefield, around 9.30am yesterday.
Mr Collinson, who lives in Micklefield, goes on the bus to neighbouring villages, such as Garforth and South Milford, and into Leeds city centre. He is also known to go for long walks.
Detective Sergeant Dave Parkin, of Leeds District CID, said: “Ian has various health issues and we are very concerned for his welfare. We are conducting a range of enquiries and carrying out searches to find him and we would like to hear from anyone who has seen him since yesterday morning or who has any information that could assist us in tracing him.”