Their call comes following the screening of BBC docu-mentary The Street, which focuses on the city's busiest night spot, Sauchiehall Street.
Glasgow Taxis Ltd say the show raises a number of concerns about public safety, particularly on weekend nights.
The firm admits that while the programme - which has attracted criticism from local traders - does not show the full picture of city centre nightlife, it can play a "positive role" in helping improve public safety.
The black-cab company already helps manage four stewarded and CCTV-monitored Nite Zone ranks across Glasgow at weekends.
But they say more ranks are needed to meet demand, including at Holland Street near Bath Street.
The firm has now vowed to "step up" its campaign to gain more rank capacity in and near Sauchiehall Street to give revellers more chance to secure a "quick and safe journey home".
Stephen Flynn, vice chairman of Glasgow Taxis Ltd, said: "We have a 10-vehicle rank outside The Garage which works well but beyond that we have little rank space to service the other pinch points, in particular further up Sauchiehall Street, before the pedestrianised section.
"What we'd hope to achieve is increased rank space, at Holland Street and elsewhere, to help us serve the night-time economy and make sure Glaswegians, visitors and tourists can enjoy accessibility, speed and safety when using taxis, especially late at night."
Glasgow Taxis Ltd, which is the biggest black cab firm in Scotland and largest in the UK outside London, added it will now continue to work with the council in a bid to secure more rank space.
A spokesman for Glasgow City Council said: "While we appreciate Glasgow Taxis' commercial concerns, we have to balance the needs of a number of road users.
"We have regular meetings with Glasgow Taxis and other organisations using the city's roads."