The 31-year-old revealed to the Evening Times that she was approached from behind by a man on Sunday April 6.
She was going home from work around 8.30pm when she turned around to see the man with his trousers undone.
A 27-year-old woman was assaulted in the same park a fortnight later and police are yet to make any arrests, despite several appeals for information.
The woman, who works in the city centre, was approached as she entered Glasgow Green from Monteith Row.
She said: "I turned around as I was getting my keys out of my bag and there was basically a guy right behind me.
"He had his trousers undone and pulled down, obviously ready to pounce when I got to the trees. Luckily for me I scared him and he bolted the other way.
"Two weeks later a girl was sexually assaulted at the same location and she managed to break free.
"I don't know if he was built up with frustration and got so brutal that it was like 'you're not getting away from me this time'."
The woman has demanded a crackdown by police following a series of sex attacks in Glasgow.
Separate inquiries are ongoing into assaults in Toryglen on May 12, Kelvingrove Park on May 30, Poundland in Sauchiehall Street on the same day, and two attacks in Govanhill, one on February 23 and a second in on May 19.
The woman who was targeted on April 6 said: "I'm so messed up just now with all of this. It needs to stop. It's ridiculous.
"They spend millions on the Commonwealth Games yet you can't even walk home by yourself and be safe."
The woman, who lives alone, also revealed she has been too afraid to return to her flat since the incident.
A spokeswoman for Police Scotland confirmed that no arrests have been made in connection with the assault on the 27-year-old woman at Glasgow Green on April 19.
The spokeswoman also said inquiries are ongoing into the incident on April 6.
She added: "There is nothing to suggest these incidents are linked."