Nadav was the eldest son of Aharon HaKohen and Elisheva, daughter of Aminadav of the tribe of Judah. His brothers were Avihu, Elazar and Itamar. As Aharon's firstborn, he would have been expected to succeed his father as High Priest.

Together with his brother Avihu, he accompanied Moshe, Aharon and seventy elders up Mount Sinai, where they beheld the Divine presence.

On the eighth day of the priestly consecration, which according to Rashi was Rosh Chodesh Nissan, the day the Mishkan was erected, Nadav and Avihu each took his fire pan and "offered before God alien fire, which had not been enjoined upon them." Fire came forth from God and consumed them. Moshe said to Aharon: "This is what God meant by saying: Through those near to Me I show Myself holy," and Aharon was silent. Rashi explains that he was rewarded for his silence: the next Divine address, forbidding priests to serve after drinking wine, was spoken to him alone.

The Sages offered many explanations of their sin: according to Rabbi Eliezer, they ruled on a point of law in the presence of their teacher Moshe; according to Rabbi Yishmael, they entered the Sanctuary after drinking wine; the Midrash Vayikra Rabbah lists twelve. The Or HaChaim, by contrast, sees their death as the result of an attachment (devekut) so intense that, out of love for the holy, they drew near to the supernal light without holding back, and died of it.

Nadav and Avihu had no sons, and it was their brothers Elazar and Itamar who carried on the priesthood.