Six patients at Frenchay Hospital are being injected with their own stem cells in the hope that they will repair damage to the brain.
Approximately 60,000 people in the UK suffer from MS, an incurable disease of the nervous system.
Prof Neil Scolding, of the Institute of Clinical Neurosciences, said: "We know stem cells are attracted into the brain, into these areas of damage."
He added that he hoped the stem cells would "help those areas to stop getting worse" and "repair damage".
'Lot of hope'
Liz Allison, an MS patient taking part in the trial, said: "I'm hoping there will be some improvement."
BBC health correspondent Matthew Hill said: "We've already seen stem cells used on cardiac patients but this is the first time a reputable organisation has tried it out on MS patients.
"There is a lot of hope riding on these trials but it is very early days yet."
He added that it was likely to be several months before any conclusions could be drawn regarding the treatment.
Source: BBC News