Marjorie Reardon was last seen at about 2.30pm on April 27, when she left her home address in Southcroft Walk, just off Abbeydale Road.
The 80-year-old has not been seen or heard from since and a police spokesman said 'both officers and her family are growing increasingly concerned for her welfare'.
She is described as being 5ft 6ins tall, of medium build with shoulder length black, greying hair.
Marjorie is believed to be wearing a green and white summer dress, a purple cardigan and pink socks when she went missing.
Officers believe the may also be wearing a pink fleece and carrying a white/cream coloured handbag.
Marjorie is known to frequent Meersbrook Park and the Abbeydale area.
Have you seen Marjorie? If you have any information, please call police on 101 quoting incident number 542 of April 28, 2016.