Marion Turner, aged 71, was last seen at 7.30am on Thursday 24 November 2011 by her husband at their home in Grosvenor Park Road.
He reported her missing a few hours later when she failed to attend an appointment at the Orchard Care Home.
Officers are concerned for her welfare as she suffers from depression and has been missing overnight.
Marion is described as white, around 5ft tall, with a stocky build, a tanned complexion and short, mousey coloured hair which is greying slightly.
It is not known what she is wearing but it is believed that she may have a three-quarter length fawn-coloured coat with her.
Police would like to hear from anyone who knows where Marion is or has seen her in the past 24 hours.
PC Jennifer Doyle, of Ripon Safer Neighbourhood Team, said:
We are concerned that Marion has been missing for over 24 hours now and we are very keen to locate her and ensure that she is safe and well.
Marion has some money and her bus pass with her, so we believe that wherever she has gone she has used public transport to get there.
I am appealing to all members of the public to keep an eye out and let us know as soon as possible if they see someone matching Marion’s description.
I would also ask Marion to get in touch if she sees or hears this appeal and let all the people that are worried about her know that she is ok.
Marion has been missing before and has previously been found in Skipton and Liverpool, however she likes to travel and it is believed that she may be anywhere in the country.
Anyone who can help the police with their enquiries is urged to call North Yorkshire Police on 0845 60 60 24 7, select option one, and pass on information for the attention of PC Jennifer Doyle or Ripon police, quoting reference number 12110198644.