The sheriff and mayor of Cocoyashi Village (Coco Village in the 4kids version), which is Nami's home town. He is like a father figure to Nami and Nojiko since they were kids and he knew their adoptive mother, Bellemere, quite well. He also kept the town together after Arlong took over the island, making sure everyone was safe and able to pay their tax.
Genzo wears a pinwheel on his hat because he used it to make Nami laugh when she was a baby (this pinwheel also inspired an attack for Luffy during their fight with Arlong). He played a role in rescuing Luffy after Arlong threw him into the ocean. All of Genzo's scars are from his first encounter with Arlong when he tried to stop him from taking Nami, Arlong made Kuroobi cut every part of his body with a sword. He was also almost killed by Arlong for hoarding novelty swords, until Usopp saved him.
Genzo's pinwheel inspired Nami's new tattoo--a pinwheel to represent him with a tangerine to represent Bellemere. After Nami sails off with Luffy and crew, Genzo says he no longer needs his pinwheel, placing it by Bellemere's grave. The origin of the pinwheel is then revealed. Bell-Mere said that Nami cried when she saw Genzo because he looked scary, but then Genzo put his pinwheel on to make Nami laugh. It is revealed later in the manga that Luffy is very interested in the pinwheel {this inspires a new attack for Luffy, Gomu Gomu No Pinwheel}, not even noticing the Navy who are trying to find Nami, just Genzo's pinwheel. However, this could be a put down in reference to Luffy's simple-mindedness. He threatens Luffy that if he finds out that he made Nami cry, he'll come after him. However, Luffy lived up to that promise, as Nami's sister, Nojiko pointed out.
Genzo appears again later, and is outraged by Nami's wanted poster, wherein she is in a bikini, saying she'll get more suitors than bounty hunters, yet has blown it up poster-sized hanging in his house.