The five-storey Centre for Student Life would be built in front of the students' union on Park Place.
The university said it would be at "the heart of the campus" and include a welcome-point for students and the public, a 550-seat lecture theatre, study space and retail outlets.
Subject to planning approval, the building would open by 2019-2020.
The proposed building would cover the 1970s students' union building as well as 46 to 49 Park Place.
The university has launched a public consultation for feedback on the plans.
A statement on the university's website said: "Working in partnership with the students' union, Cardiff University wishes to build an iconic building at the heart of the university to deliver a world-leading student experience covering every facet of student life."
Plans for a new building have been unveiled by Cardiff University as part of a multi-million pound investment.