The device has "wings" that push downwards rather than flap, mimicking the pulsing movements of a swimming jellyfish.
The machine may lend itself to the development of small unmanned drones for reconnaissance and rescue missions, or monitoring traffic and air pollution.
Previous attempts to design a mini-flying machine have focused on the flight of insects such as dragonflies.
But the wing-flapping motion of insects suffers from a major problem that presents a challenge to human engineers—it is inherently unstable.
Insect-like drones end up being over-complex, requiring active control systems or high-drag tails and sails to stabilise them.
In contrast, the flying jellyfish is intrinsically able to keep upright and recover from disturbances during hovering and other manoeuvres.
The four-winged prototype tested by the scientists is four inches long, weighs 0.07oz, and is controlled by wire from the ground.
Writing in the Journal Of The Royal Society Interface, the team, led by Dr Leif Ristroph from New York University, concluded: "These results show the promise of flapping flight strategies beyond those that directly mimic the wing motions of flying animals."