A study of 674 people with an average age of 80 showed that those following a Mediterranean-like diet had larger brains.
By volume, they had five millilitres more nerve cells and 6.41 millilitres more nerve fibres than those with different dietary habits.
Mediterranean diets include low consumption of saturated fatty acids, dairy products, meat and poultry, and mild to moderate intakes of alcohol.
Eating more fish and less meat was also associated with less brain shrinkage, the US study found.
“These results are exciting, as they raise the possibility that people may potentially prevent brain shrinking and the effects of ageing on the brain simply by following a healthy diet,” lead scientist Dr Yian Gu, from Columbia University in New York, said.
Dr James Pickett, head of research at the Alzheimer’s Society, said: “There is an increasing amount of evidence that eating a healthy diet, rich in fish, vegetables, legumes and nuts is good for your brain.
“This study delves further into the potential benefits that diet could have, but it does not prove that a Mediterranean-style diet can stop your brain from shrinking as you age.
“Other key ways to keep your brain healthy is to take as much physical exercise as you can, stop smoking and keep your blood pressure in check.”