The proposals, submitted by developer Watkin Jones Group, aim to redevelop a vacant 0.06-hectare site in the city centre to deliver the tower, which would comprise student accommodation and retail/commercial space, alongside landscaping, ancillary and community facilities.
According to a letter accompanying the application, the tower would be the tallest in Wales.
It added that the site sits around 100 metres from the main shopping area, and around 300 metres from Cardiff Central rail station and the city bus station.
The letter added: "There has been considerable support and excitement for the development of the tallest building in Wales on this site and it is considered to be an appropriate location for such an iconic building."
Iain Smith, group planning director at Watkin Jones Group, told Planning that, subject to permission, work could begin on site next year for completion in August 2018.
He added: "If you look at Cardiff at the moment, there is a massive amount of development going on. It’s a really exciting place to be and to be developing in. And this project just adds to that."