Karen Seymour-Fairey, 65, was last seen leaving her home address in Boscombe on Monday 27 May 2013, when she left the premises carrying a rucksack.
Her flat and car were both left unlocked.
Inspector Steve Thorpe, of Bournemouth police, said, “Karen has recently been unwell and concern is growing for her welfare.
“Karen’s family are extremely worried about her and I would urge anyone who knows of her whereabouts to contact Dorset Police as soon as possible.
“I appeal to Karen to contact us, or someone she knows, to let us know that she is safe and well.”
Karen is described as five feet six inches tall with short brown curly hair. She has blue eyes, wears glasses and speaks with a slight Yorkshire accent.
Anyone with any information or knowledge as to Karen’s whereabouts should call Dorset Police on 101 quoting the number C:13:C:20984.