The man, described as being in his 20s, entered the Ladbrokes in Fernbank at around 6pm on Sunday.
He threatened two members of staff with an axe and jumped over the counter to steal a large sum of money.
He then fled the premises, using a lane at the side of the building to make his getaway.
The suspect is described as wearing a light coloured sweatshirt, blue jeans, and black trainers.
His face was covered by a green and white scarf, and he spoke with a local accent.
A police spokesman said: “While no-one was injured, the staff who were working at the bookmakers were understandably shaken as a result of their ordeal, and we are keen for any information that can assist us in tracing the suspect.
“Anyone who was in the area of Fernbank around the time the robbery took place, who may have noticed the suspect there, should contact police immediately.
“Similarly, anyone who recognises his description, or has any other information that can help our inquiries, should also get in touch.”
Anyone with any information is asked to contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.