Though the two of them get along fine, Luffy is utterly terrified of his grandfather Garp. This is due to the extreme training he was put through in his younger years in his bid to make Luffy a Marine, as well as Garp’s tendency to punch Luffy to discipline him.
Garp had high expectations for Luffy, but to Garp’s dismay, Luffy did not share his grandfather’s plans for his future. However, Garp respects Luffy as a great person, even if he is a pirate. He often brags about Luffy to his superior Sengoku, laughing whenever Luffy does something audacious and is prone to saying “That’s my grandson” much to Sengoku’s exasperation.
When Sengoku was talking with Garp and Kuma, Garp said that Luffy is not the type of person to brag about defeating someone, arguing that Bartholomew Kuma did not need to kill Luffy to keep Moria’s defeat a secret. When Luffy entered the battle of Marineford, Garp recognized him and looked shocked and horrified at the sight of his grandson entering the fearsome battle. Later, as the battle rages on, Garp merely looks resigned as his grandson furiously makes his way to the execution platform. When Luffy came close to the platform, Garp stands in his way in the name of his Marine duties. However, in the end, Garp chose family over his duties as he allowed Luffy to hit him and reach the execution platform to save Ace.
He also tried to attack Admiral Akainu when Ace was killed by the admiral and Luffy was on the verge of being killed as well, but was stopped by Sengoku.
As Garp has resigned from the Marines, he and Luffy are no longer enemies by law.