The event is being held in the City Chambers on Monday and there will be representatives from more than 30 private firms, the council and its external organisations.
The fair is the latest drive of the council's £50million Glasgow Guarantee,which is aimed at ensuring all people aged 18-24 have access to a job, apprenticeship or training.
Council leader Gordon Matheson said: "Glasgow's young graduates will play a hugely important role in the future prosperity of the city.
"So it makes sense both economically and socially to support them as they begin their working life.
"Glasgow is home to many highly skilled and qualified graduates whom we would like to stay in the city to develop their careers.
"The council's first graduate recruitment fair is a great opportunity to take the next step towards a successful future."
The Glasgow Guarantee includes the Commonwealth Apprenticeship Initiative, the Commonwealth Graduate Fund, the Commonwealth Jobs Fund and the Commonwealth Youth Fund.
More than 3000 young people have gained jobs, apprenticeships and training over the past four years through these projects.
The jobs fair will take place between 10am-4pm in the banqueting hall.
Anyone interested in registering for the event should see the website: glasgow. mappit.org.uk