Lilian Brown, 73, was attacked in Butts Street just before 7 pm on Saturday night while she was walking home.
But the grandmother was not giving up her purse without a fight and chased after the mugger, despite suffering from asthma.
She was unhurt but has been left shocked by the incident and is hoping police will catch the culprit, whom she describes as aged about 20 and wearing dark clothing.
Lilian said: “He was dressed in this jacket that was far too big and had a hood, you could not really make him out at all.
“I’d seen him on the High Street and he ducked into M and Co entrance and then when I got to Johnstone Street I could not see him.
“Then he just took my purse and ran off, I actually ran after him.
“He was off like a shot.”
She’s relieved that there was only £3 in her tan coloured purse, but has had to cancel her banks cards this week.
Lilian had just left the rugby club when it happened and initially she gave chase, but only made it a short distance, before he disappeared into Johnstone Street.
Determined not to be victimised, she added: “I am just telling myself it was a one off, worse things have happened to me.
“But I will be taking a taxi from now on.
“I just want to warn folk to be more aware of their surroundings, it was only just after six but it was still dark.”
Police in Annan are investigating and have appealed for witnesses to the theft.
Constable Scott Lisett said: “This was a despicable theft which has left the victim in a state of shock.
“We are appealing to any- one who may have been in the Butts Street area to get in touch if they can help us identify this man.
“He is described as being about 20-years-old, about ve foot tall, and was wearing a large black jacket with the hood up.
“This man may have been hanging around the Butts Street/High Street area prior to this theft taking place.”
Callers can contact the 101 number and should quote the reference number 3543 of 3/11.
