The grandfather of Max Payne was the father of his mother Helen Payne and the father-in-law of Jack Payne.
He used to tell his grandson of Greek myths, alongside his daughter. He later comforted Max when Helen died in 1976.
Max’s grandfather’s fate is left unclear, but considering that he appeared to be in his 60s in the comics, it can be assumed that he passed away, sometime before or after Max Payne.