The service, Person to Person, was launched to tackle the loneliness and isolation that charities say is often the experience of older people on the autism spectrum.
National Autism Society Scotland is training volunteers to help build confidence and social skills.
This can include outings and activities, phone calls to catch up on news and support in achieving goals.
Douglas Herbertson, 54, from Springburn, has become friends with Harry Ewing, 65, from Newton Mearns, through the project.
Mr Herbertson, who was diagnosed with Asperger syndrome at the age of 50, said: "I often felt very lonely until I met Harry. I wanted some company and friendship, but I wasn't sure where to start. Meeting Harry has made a big difference.
"One of the best things has to be having a laugh and a joke with Harry. It felt like such a long time since I'd had a friend to laugh with; it's almost learning how to do it all over again. Harry is great company."
Mr Ewing said: "I discovered Douglas is an intelligent, interesting man, and there are lots of things he would like to do.
"He just needed someone to say: 'Take your time. Have a think and if it feels right, go for it'."