Emergency services were called to the incident in George Street at around 6.20pm.
The woman, believed to be in her 40s, died at the scene.
The 48-year-old man driving the bus was not injured.
A police spokesman said: “Around 1820 hours this evening, Saturday 28 October 2017, a woman, believed to be in her 40s, was fatally injured after being struck by a double decker First Bus as she crossed George Street in Glasgow City Centre.
“Emergency services attended but she died at the scene.”
Part of George Street was closed while police carried out investigations.
A First Glasgow spokesman said: “Our thoughts go out to all the people involved in this tragic incident.
“We will continue to work with the police as they carry out their investigation.”