Catherine Lynn, 81, was last seen at 3.30pm yesterday when she was out walking in Whitecrook Street, Clydebank.
The pensioner, known as Cathleen, was reported missing by her daughter.
Police Scotland said Mrs Lynn, who is from Clydebank, suffers from dementia and there is concern for her welfare.
Her family are said to be "extremely worried".
Police Scotland said extensive inquiries have already been carried out to trace her but efforts have so far proved unsuccessful.
The missing woman is described as 5ft 1in, of stocky build, with short, curly brown hair. She wears glasses and a hearing aid.
Mrs Lynn was last seen wearing a black cardigan, black skirt, black shoes and a three quarter length turquoise jacket. She also has a walking stick.
Police are asking for the public's help to find the pensioner.
Inspector Donald Leitch said: "Cathleen's family are extremely worried and we have been carrying out extensive inquiries in trying to locate her.
"I am appealing to anyone who may have seen Cathleen or who has any knowledge as to her whereabouts to contact us as a matter of urgency."
Anyone with information is asked to contact Dumbarton Police Office on the police non-emergency number, 101.