Taken while healthy, the test involves drawing lines between numbers in ascending order as fast as possible.
Men who scored in the bottom third were about three times as likely to die after a stroke compared with those who were in the highest third.
The study looked at 1,000 men between the ages of 67 and 75 over 14 years.
Of the 155 men who had a stroke, 22 died within a month and more than half within an average of two- and-a-half years.
The researchers think that tests are able to pick up hidden damage to brain blood vessels when there are no other obvious signs or symptoms.
Silent injury
Dr Clare Walton, from the Stroke Association, said: "This is an interesting study because it suggests there may be early changes in the brain that puts someone at a greater risk of having a fatal stroke.
"This is a small study and the causes of poor ability on the drawing task is not known. Although much more research is needed, this task has the potential to screen for those most at risk of a severe or fatal stroke before it occurs so that they can benefit from preventative treatments."
Dr Bernice Wiberg, lead author from Uppsala University in Sweden, said: "As the tests are very simple, cheap and easily accessible for clinical use, they could be a valuable tool – alongside traditional methods like measuring blood pressure (and) asking about smoking – for identifying risk of stroke, but also as a possible important predictor of post-stroke mortality."
She also suggested it could help improve information given to patients and their family.
More than 150,000 people suffer a stroke every year.