They said their set-up could someday be adapted to help disabled people operate a motorised wheelchair or an artificial limb.
Experiments have allowed a monkey to control a computer with its thoughts using electrodes implanted into the animal's brain.
This experiment, reported in the Proceedings of the National Academy of Sciences, required no surgery and no implants.
"The results show that people can learn to use scalp-recorded electroencephalogram rhythms to control rapid and accurate movement of a cursor in two dimensions," Jonathan Wolpaw and Dennis McFarland of the New York State Department of Health and State University of New York in Albany wrote.
They tested their device on four people - two partly paralysed men who used wheelchairs and a fully mobile man and woman.
During the experiments, the four volunteers faced a video screen wearing a cap that held 64 electrodes against the scalp to record brain activity.
The key was a special computer algorithm - a programme that translated the brain signals into a meaningful directive of what the users wanted the computer to do.
It took some practice, but all four learned to move a cursor on the screen in two directions, Wolpaw and McFarland found.
Volunteers learned to move a
cursor on screen in two directions
"The impressive non-invasive multidimensional control achieved in the present study suggests that a non-invasive brain control interface could support clinically useful operation of a robotic arm, a motorised wheelchair, or a neuroprosthesis," the researchers wrote.
The two disabled men were better at the task, the researchers found.
This could have to do with stronger motivation or perhaps a brain forced to be more adaptable to cope with the injuries that left the men disabled, the researchers said.
Many groups are working on ways to help disabled and paralysed people use their thoughts to control machines. While some require brain implants, others use such cues as eye motion or brainwaves recorded from outside.