ComfortDelGro's flat fare option, which was launched yesterday, has already received 2,000 bookings; and the firm expects the volume to grow further.
'Dynamic pricing', as used by GrabCar and Uber, means private-hire cars are generally cheaper than taxis during off-peak hours and after midnight.
More commonly known as surge pricing, a system already in use by ride-hailing service Uber, the move will see fares fluctuate according to demand.
Grab will be rolling out a new taxi service - JustGrab - which will provide fixed upfront fares when booking a taxi but will also be subject to surge pricing.
During major rail breakdowns, commuters have complained of Uber fares exceeding $140 - four to five times that of a usual taxi fare.
The growth of Singapore's rental car population remains in the fast lane, fuelled by private-hire players such as Uber and Grab.
The new upfront fare system shows users the exact amount they have to pay before they take a ride, replacing the old fare estimate and surge pricing system.
Powered by ride-hailing apps like Uber and Grab, the private-hire car market has surged in the last year and a half, and looks set to grow even more.
With the rise of ride-booking services like Uber and GrabCar, more than 24,500 rental cars are on the road as of August, a 38 percent increase from last year.