They say the vehicle, heading westbound, went off the road and crashed into a tree.
The female driver, the sole occupant of the vehicle, was taken to hospital in critical condition.
EMS says the woman, in her 20s, suffered serious head injuries.
Investigators are working to determine if alcohol or speed were factors in the crash.
Police say charges may end up being laid.
After that crash, police say there was another incident in the eastbound lanes near the first scene.
Investigators say another driver had slowed down in an attempt to stop to help them victim of the first crash when they were hit as well.
“She ultimately slowed down her vehicle and, in doing so, happened to cut across the left hand lane and was hit by an oncoming vehicle coming from the same direction,” said Acting Sergeant Jeff Leimer with the Calgary Police Service.
No one was injured in the second crash.
The westbound lanes of Glenmore Trail remain closed and there are traffic restrictions in the eastbound lanes as well. There is no timeline on when it could reopen. The crash is in the same area as a fatal crash that took place a month ago, on the Easter weekend.