Patients with Pelizaeus-Merzbacher disease struggle to produce a fatty sheath around their nerves, which is essential for function.
A study, published in Nature Medicine, showed that a high-cholesterol diet could increase production.
The authors said the mice "improved dramatically".
Pelizaeus-Merzbacher disease (PMD) is one of many leukodystrophies in which patients struggle to produce the myelin sheath. It protects nerve fibres and helps messages pass along the nerves.
Without the sheath, messages do not travel down the nerve - resulting in a range of problems including movement and cognition.
Researchers at the Max Planck Institute of Experimental Medicine, in Germany, performed a trial on mice with the disease and fed them a high cholesterol diet.
The first tests were on mice when they were six weeks old, after signs of PMD had already emerged. Those fed a normal diet continued to get worse, while those fed a cholesterol-enriched diet stabilised.
"This six-week-long cholesterol treatment delayed the decline in motor co-ordination," the scientists said.
Further tests showed that starting the diet early was more beneficial, leading the researchers to conclude that in mice "treatment should begin early in life and continue into adulthood".
This study was only in mice, meaning it is not known if there would be a similar effect in people - or if there would, how early treatment would have to start.
The authors of the report said: "Dietary cholesterol does not cure PMD, but has a striking potential to relieve defects."
It is thought the cholesterol frees up a "traffic jam" inside cells in the brain. The disease is caused by producing too much of a protein needed in myelin, which then becomes stuck inside the cells. It is thought the extra cholesterol helps to free up the protein.