Daniel Madden smashed the window of Christina McKellar's back door and forced his way into the house.
The 33-year-old stole jewellery, including his late grandfather's bracelet, cash from a piggy bank and cigarettes worth almost £500 from the house in Shettleston.
But when he tried to pawn the jewellery in a shop, his cousin, who had heard about the break-in, went to the police.
Madden, of Easterhouse, pleaded guilty at Glasgow Sheriff Court to breaking into Mrs McKellar's home in Ardgay Street and stealing from her.
Sheriff Martin Jones QC told Madden the fact he "stooped so low" as to steal from his elderly grandmother was something he would have to live with.
The jewellery was recovered following the May 19 theft and the remaining £190 was eventually repaid to Mrs McKellar by Madden.
Defence lawyer Paul Mullen said his client accepts he had "sunk low" and the crime was committed to fund a drug habit.
The court heard that Mrs McKellar left her house around 2.20pm on May 19 and arrived home at 4pm that day to discover that a glass panel in her back door had been smashed.
Coins were missing from a piggy bank and jewellery had been stolen from her wardrobe.
When he was caught with the items, cautioned and charged by officers, Madden replied: "It's all a mistake."
Speaking after the case, Mrs McKellar said: "When he was growing up I was very close to him, he was my baby.
"I think he regrets what he has done."