Garry Kane, 41, left, must serve at least 17 years before being eligible to apply for parole.
Kathleen Milward, 87, was beaten to death in her bungalow in Stonehouse, Lanarkshire, on January 3, 2012, by drug-addict Kane who was desperate for a fix.
Today at the High Court in Glasgow judge Lord Matthews told Kane: "You were found guilty of the murder of your own grandmother. No words of mine can bring home the enormity of that.
"What made it more heinous was that she was murdered in her own home."