Takao Osugi is the father of Suzuno Osugi, the Priestess of Byakko.
In Fushigi Yuugi Genbu Kaiden, Takao is a handsome young man who is a good friend of the Okuda family and has great respect for Einosuke, his mentor, as a scholar. He's happily married to Tamayo Osugi and by the time Genbu Kaiden takes place, their daughter Suzuno is already eight years old and greatly admires Takiko, whom she sees as a big sister figure.
He has known Takiko ever since she was a little girl, and she was in love with him but he was oblivious to it. When Takiko blurted out her feelings, Takao was sincerely stunned.
After his initial appearance, Takao has to return home because Suzuno has fallen ill. He is seen again at the end after Einosuke committed suicide and Takiko has died inside the book; Takao has returned to the Okuda household in Morioka, having been told that Einosuke's corpse has been found but Takiko is still missing. He finds the Universe of the Four Gods manuscript and a letter containing Einosuke's will; he reads both letter and book and is moved to tears by his newfound knowledge.
In Fushigi Yuugi: Byakko Senki, set a few months after the end of Genbu Kaiden, Takao is the owner of the Universe of the Four Gods, which Einosuke entrusted him with. He tried to destroy it so no more tragedies like that of the Okuda family will happen (and to protect Suzuno and other girls from being potential Priestesses), but all the methods he used (using an industrial kiln from his workplace, sealing it in a Shinto shrine, etc.) have failed spectacularly due to the book's own magic. He and Tamayo are also deeply worried and burdened by what they know about the Book and the true reason behind the deaths of Takiko and Einosuke.
When Takao is pondering about either throwing the Universe into the nearby ocean or burying it in the mountains, the Great Kanto Earthquake of 1923 takes place and destroys Tokyo. Tamayo is fatally crushed by the debris of the Osugi home and Takao is severely injured, but Suzuno is unharmed thanks to the Book itself and its powers. Realizing that Suzuno will be safer inside the Book than in Tokyo, Takao uses his last minutes of life to send Suzuno inside it for her own protection, telling his daughter about Takiko's adventures inside it and reassuring her about his and Tamayo's love for her.