Cameras recording outside the aircraft will display pictures on the screens.
Spike Aerospace, which is designing the plane, says drag will be reduced by removing windows, which "cause significant challenges in designing and constructing an aircraft fuselage".
The S-512 supersonic jet is not expected to launch until 2018.
In a blog on its website the company said windows required additional structural support and added weight to the aircraft but these problems could be eliminated by using micro-cameras and flat displays.
Cruising speed
It plans to surround the aircraft with cameras and display the views on the cabin screens. Passengers will be able to dim the screens or change the images.
Dr Darren Ansell, an expert in space and aerospace engineering at the University of Central Lancashire, said that the experience for passengers of being in a plane without windows could be an unusual one.
"There will be no natural light - it will all be simulated - so it will be a bit like being in a tube. And how would it work from a safety perspective? If there was an accident how would you know which way the plane was facing, and where you had landed, when the cameras have failed?" he said.
Spike Aerospace is based in Boston in the US and is made up of a team of engineers who have experience of aircraft design and building.
In December, it announced plans for the S-512, which it claimed would be the world's first supersonic business jet.
Expected to cost $80m (£48m), the jet will carry 18 passengers and the company claims it will be able to fly from New York to London in three to four hours rather than the six to seven it currently takes.
It will have a cruising speed of Mach 1.6 and a maximum speed of Mach 1.8. In comparison, a Boeing 777-300 has a cruising speed of Mach 0.8.
Other firms are racing to develop similar supersonic jets, including Aerion and Gulfstream.
From BBC
From BBC
