James Henry Alden is Henry's, Jessie's, Violet's and Benny's kind and wealthy paternal grandfather, whom they live with in an unidentified New England state (most likely CT, MA, or RI based on the books). In the first book after the children's mother and father died, the children ran away, afraid that he might not like them and that he was mean because he did not see much of their mother, his daughter in-law. His son's name is unknown, but it is likely that it started with a 'J' in keeping with family tradition.
He has one sister who is about 1 year older than he is, Aunt Jane, and a brother who was several years (15-20 years) younger than he is (unnamed). This younger brother is Joe Alden's father. James is said to own several mills (paper, plastic, etc), refineries, a woodlot, a boat, a private island, a private plane, a farmhouse outside of Boston, a ranch house in Pennsylvania, and is the main patron of the town museum.
It is hinted that his favorite color is yellow, and it is implied that he is almost 70 years old in book 3.