Narokobi was born around 1943 in Wautogik village, East Sepik Province, Papua New Guinea, to his father Anton (Kukum) Narokobi and mother Maria Mokoi and was the second eldest of five siblings. His siblings were Veronica, Apolonia, Caroline and Camillus. Camillus his younger and only brother is intending to stand for the Wewak Open seat. Camillus is also a lawyer in his own right at the family law firm, Narokobi Lawyers. Narokobi's father Anton was taught by pioneer Catholic missionaries and became one of the early catechists who served the people of Boiken and Dagua villages through teaching the Catholic faith. Narokobi was a widower, having lost his wife Regina to breast cancer in 2007. He had 7 children: Vergil, Daniel, Anna, Justina, Ottonia, Benedine and Regina (twins). His son Vergil is also a lawyer and after completing a bachelor's degree in law with honours at the University of Papua New Guinea, he went on to do his Masters in law at Cambridge University. His daughter Anna has also recently completed her degree in law in Australia.