The 35-year-old victim was walking east along Brunton Terrace, off London Road, when a man approached from behind and pushed her while attempting to grab her bag.
She struggled with her attacker before he made off empty-handed towards Montgomery Street.
Police who are now appealing for anyone who witnessed the incident, which took place at around 4.50pm on Monday, to come forward.
The suspect is described as white, 20 to 30-years-old with a medium build. He was wearing dark jeans, a bomber jacket and a flat cap.
A police spokesman said: "Anyone who recognises his description is asked to contact us immediately."